From f25478dad6d96dcdaf80e8201d0f80cc894f3267 Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 07:24:24 +0100 Subject: [PATCH 1/8] Add golden tests for strategic-form logit QRE. --- .../golden_logit/strategy_agg_2x2.json | 45 ++ .../strategy_bagg_coffee_3_2_2_3.json | 473 ++++++++++++++++++ ...trategy_coordination_2x2_to_lambda_20.json | 122 +++++ .../strategy_random_3_player_6x6x6.json | 87 ++++ .../strategy_random_4_player_4x4x4x4.json | 92 ++++ .../strategy_random_bimatrix_20x20.json | 165 ++++++ .../strategy_stripped_down_poker.json | 94 ++++ tests/test_logit_golden.py | 55 +- 8 files changed, 1124 insertions(+), 9 deletions(-) create mode 100644 tests/test_games/golden_logit/strategy_agg_2x2.json create mode 100644 tests/test_games/golden_logit/strategy_bagg_coffee_3_2_2_3.json create mode 100644 tests/test_games/golden_logit/strategy_coordination_2x2_to_lambda_20.json create mode 100644 tests/test_games/golden_logit/strategy_random_3_player_6x6x6.json create mode 100644 tests/test_games/golden_logit/strategy_random_4_player_4x4x4x4.json create mode 100644 tests/test_games/golden_logit/strategy_random_bimatrix_20x20.json create mode 100644 tests/test_games/golden_logit/strategy_stripped_down_poker.json diff --git a/tests/test_games/golden_logit/strategy_agg_2x2.json b/tests/test_games/golden_logit/strategy_agg_2x2.json new file mode 100644 index 000000000..7732205b4 --- /dev/null +++ b/tests/test_games/golden_logit/strategy_agg_2x2.json @@ -0,0 +1,45 @@ +{ + "counts": [{"predictor_attempts": 39, "accepted_steps": 39, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 77, "function_evals": 77, "jacobian_evals": 40, "factorizations": 40}], + "points": [ + [0.0, 0.5, 0.5, 0.5, 0.5], + [0.00109028013333371, 0.4925063625415017, 0.5074936374592074, 0.4925063625415017, 0.5074936374592074], + [0.0022449455763905732, 0.48426911358557934, 0.5157308864156755, 0.48426911358557934, 0.5157308864156755], 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0.30642836892923436], + [13.666299784918671, 0.37283017832188503, 0.6271698091812338, 3.8249137891045905e-09, 6.434217482191897e-09, 0.6920378014826816, 0.30796219858915225], + [15.02539085192333, 0.36893448359724695, 0.6310655132359876, 6.146792017375439e-10, 1.051413904544232e-09, 0.6904837111911637, 0.3095162888662963], + [16.521244597404575, 0.36541960596862266, 0.6345803928097824, 8.243530661275447e-11, 1.4315550779781826e-10, 0.6889376959525474, 0.31106230408885316], + [18.16747155927346, 0.3622528944109426, 0.6377471049082524, 9.059196211571772e-12, 1.594873704493214e-11, 0.6874216827661652, 0.3125783172618039], + [19.97904480218972, 0.3594027295061036, 0.6405972700623276, 7.995798384488174e-13, 1.425166309702416e-12, 0.6859521201222377, 0.3140478798958814], + [21.972437281489878, 0.3568391249091959, 0.6431608748105772, 5.5442909057015637e-14, 9.992937265561177e-14, 0.6845408736805124, 0.3154591263309307], + [24.165772564487053, 0.3545340838690573, 0.6454659159485654, 2.947842599243011e-15, 5.3668519049788984e-15, 0.6831960484258619, 0.31680395158129265], + [26.578990324639648, 0.35246177483772073, 0.6475382250435545, 1.1701712920228832e-16, 2.1498235994024811e-16, 0.6819227177745057, 0.3180772822299967], + [29.234028156758118, 0.35059857813577977, 0.6494014217868397, 3.367750966239748e-18, 6.237966729155149e-18, 0.6807235533992038, 0.3192764466036996], + [32.1550214057302, 0.34892304458518547, 0.6510769553642622, 6.80400483781028e-20, 1.2696010833425245e-19, 0.6795993580542624, 0.3204006419476881], + [35.36852285949594, 0.3474157972850109, 0.6525842026818525, 9.313547793746568e-22, 1.749452445346144e-21, 0.6785495086595247, 0.3214504913418554], + [38.903744331675796, 0.34605939955037074, 0.6539406004278164, 8.307042638375369e-24, 1.5697630111410838e-23, 0.6775723193969109, 0.3224276806041185], + [42.79282235264075, 0.34483820549518635, 0.6551617944903837, 4.625114401163039e-26, 8.787304314027327e-26, 0.6766653354177052, 0.3233346645830975], + [47.07111040203508, 0.34373820467843214, 0.656261795311969, 1.5333701207292483e-28, 2.9274960263695576e-28, 0.6758255675782303, 0.32417443242241556], + [51.77750035289967, 0.34274686843021346, 0.6572531315633627, 2.87393633629468e-31, 5.511074880405543e-31, 0.6750496778588232, 0.3249503221417058], + [56.954776059743295, 0.3418530026888343, 0.6581469973068397, 2.876196536522958e-34, 5.537351140074456e-34, 0.6743341240748074, 0.3256658759256293], + [62.65000231247775, 0.341046610189582, 0.6589533898074853, 1.4434440382958977e-37, 2.788951168591734e-37, 0.6736752713494117, 0.3263247286509491], + [68.91495269759544, 0.34031876345879136, 0.6596812365392073, 3.390198740042591e-41, 6.571634411852728e-41, 0.6730694767020615, 0.32693052329823563], + [75.80658026011902, 0.33966148912692906, 0.6603385108716959, 3.4538258458225566e-45, 6.714609365056271e-45, 0.6725131520740916, 0.3274868479261517], + [83.3875352477932, 0.339067663459697, 0.6609323365393521, 1.4038945531578321e-49, 2.736560891138376e-49, 0.6720028101971429, 0.327997189803055], + [91.72673464615505, 0.3385309186230576, 0.6614690813762806, 2.0768662871470586e-54, 4.058071979623768e-54, 0.6715350969158617, 0.32846490308429827], + [100.8999886833281, 0.338045558976887, 0.6619544410226494, 1.010679335709923e-59, 1.9790932226645663e-59, 0.6711068129025687, 0.3288931870975597], + [110.99069000084592, 0.3376064865814252, 0.6623935134182483, 1.447605567228984e-65, 2.840243229418488e-65, 0.6707149271373913, 0.329285072862711], + [122.09057175619115, 0.3372091350638697, 0.6627908649358989, 5.399973406176336e-72, 1.0613748775912108e-71, 0.6703565840602274, 0.32964341593985375], + [134.30054154916962, 0.3368494110030429, 0.6631505889967922, 4.585622868513852e-79, 9.027649765267519e-79, 0.670029105917474, 0.32997089408259006], + [147.7315987533994, 0.3365236420296774, 0.6634763579702047, 7.6451891803233e-87, 1.5072944779632169e-86, 0.6697299915138496, 0.33027000848620064], + [162.50584359232585, 0.3362285308958301, 0.6637714691040851, 2.1264335494353414e-95, 4.197936199228051e-95, 0.6694569123262194, 0.33054308767381985], + [178.7575871331531, 0.3359611148307504, 0.6640388851691883, 8.249153307500712e-105, 1.6304739816874275e-104, 0.669207706731841, 0.3307922932681895], + [196.63457228947962, 0.33571872956656806, 0.6642812704333874, 3.6652528037697327e-115, 7.252376988591149e-115, 0.6689803729391253, 0.3310196270608985], + [216.29931693257674, 0.3354989774819067, 0.664501022518061, 1.501839197604726e-126, 2.974595302663232e-126, 0.6687730610774096, 0.3312269389226086], + [237.93059132131773, 0.33529969937282283, 0.6647003006271535, 4.471416921086644e-139, 8.864165930464512e-139, 0.6685840647972513, 0.33141593520276275], + [261.72505648419894, 0.335118949854986, 0.6648810507510348, 7.442122185455956e-153, 1.4765282657470808e-152, 0.6684118128485415, 0.3315881876835527], + [287.89899808371325, 0.33495497330645563, 0.6650450271916372, 5.189342999567912e-168, 1.0303315464125765e-167, 0.668254859606622, 0.3317451408359436], + [316.69037516539765, 0.3348061870053352, 0.6651938134042542, 1.103842216813708e-184, 2.193116621190855e-184, 0.6681118778707981, 0.3318881224970642], + [348.3609275827886, 0.3346711615298452, 0.6653288388071084, 5.0526021799991065e-203, 1.0044611928934882e-202, 0.6679816496718624, 0.33201835063373736], + [383.1985693914277, 0.3345486056513127, 0.6654513946259945, 3.390118546624974e-223, 6.743292534150883e-223, 0.6678630585577005, 0.3321369416960478], + [421.52000637825904, 0.3344373523827972, 0.6655626478455042, 2.185811206268099e-245, 4.349975514903108e-245, 0.6677550819995761, 0.3322449182110236], + [463.6736152035055, 0.3343363465264139, 0.6656636536616042, 8.510902261650693e-270, 1.6945206090535836e-269, 0.667656784196285, 0.3323432159784327], + [510.04261045989153, 0.3342446335455467, 0.6657553666093431, 1.2005988475700441e-296, 2.3913775890309851e-296, 0.6675673092925399, 0.33243269085235666], + [561.0485284405513, 0.33416134961011024, 0.665838650517524, 0.0, 0.0, 0.6674858750172372, 0.33251412510288847], + [617.1550592862137, 0.33408571268174625, 0.6659142874234553, 0.0, 0.0, 0.6674117667388326, 0.33258823336072757] + ] +} diff --git a/tests/test_logit_golden.py b/tests/test_logit_golden.py index fa93b2fe0..37c5172f7 100644 --- a/tests/test_logit_golden.py +++ b/tests/test_logit_golden.py @@ -6,12 +6,14 @@ Jacobian may still yield points on the correct curve, because the corrector only drives the equations themselves to zero, but it almost always changes the steps taken. -To regenerate the reference data after an intentional change in tracing behaviour, run -``python -m tests.test_logit_golden`` from the repository root. +Reference data is generated by running ``python -m tests.test_logit_golden`` from the +repository root, which writes data only for cases that have none. To regenerate a case after an +intentional change in tracing behaviour, name it: ``python -m tests.test_logit_golden NAME``. """ import dataclasses import json import pathlib +import sys import numpy as np import pytest @@ -32,6 +34,12 @@ class GoldenCase: factory: object maxregret: float | None = None lams: tuple[float, ...] | None = None + strategic: bool = False + + +def _random_table_game(shape: tuple[int, ...], seed: int) -> gbt.Game: + rng = np.random.default_rng(seed) + return gbt.StrategicGame.from_arrays(*[rng.integers(0, 100, shape) for _ in shape]) CASES = { @@ -67,6 +75,29 @@ class GoldenCase: lambda: games.create_allpay_correlated_types_efg(gbt.Rational(3, 5), True, 11), lams=(1.0, 5.0, 20.0), ), + # Strategic-form logit, on each representation of mixed strategy profiles + "strategy_random_bimatrix_20x20": GoldenCase( + lambda: _random_table_game((20, 20), seed=1), maxregret=1.0e-4, strategic=True + ), + "strategy_random_3_player_6x6x6": GoldenCase( + lambda: _random_table_game((6, 6, 6), seed=2), maxregret=1.0e-4, strategic=True + ), + "strategy_random_4_player_4x4x4x4": GoldenCase( + lambda: _random_table_game((4, 4, 4, 4), seed=3), maxregret=1.0e-4, strategic=True + ), + "strategy_coordination_2x2_to_lambda_20": GoldenCase( + lambda: games.create_2x2_symmetric_coordination_nfg(), lams=(20.0,), strategic=True + ), + "strategy_stripped_down_poker": GoldenCase( + lambda: games.create_stripped_down_poker_efg(), maxregret=1.0e-4, strategic=True + ), + "strategy_agg_2x2": GoldenCase( + lambda: games.read_from_file("2x2.agg"), maxregret=1.0e-4, strategic=True + ), + "strategy_bagg_coffee_3_2_2_3": GoldenCase( + lambda: games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), maxregret=1.0e-4, + strategic=True, + ), } COUNT_FIELDS = [ @@ -82,14 +113,17 @@ def _point(qre) -> list[float]: def _trace(case: GoldenCase) -> dict: game = case.factory() + branch, at_lambda = ( + (gbt.gambit._logit_strategy_branch, gbt.gambit._logit_strategy_lambda) + if case.strategic + else (gbt.gambit._logit_behavior_branch, gbt.gambit._logit_behavior_lambda) + ) if case.lams is None: - profiles, stats = gbt.gambit._logit_behavior_branch( - game, case.maxregret, FIRST_STEP, MAX_ACCEL, _with_stats=True - ) + profiles, stats = branch(game, case.maxregret, FIRST_STEP, MAX_ACCEL, _with_stats=True) points = [_point(qre) for qre in profiles] else: events = [] - _, stats = gbt.gambit._logit_behavior_lambda( + _, stats = at_lambda( game, list(case.lams), FIRST_STEP, MAX_ACCEL, events.append, _with_stats=True ) points = [_point(e.qre) for e in events if isinstance(e, gbt.LogitPathEvent)] @@ -104,7 +138,7 @@ def _golden_path(name: str) -> pathlib.Path: @pytest.mark.parametrize("name", list(CASES)) -def test_logit_behavior_path_matches_golden(name: str): +def test_logit_path_matches_golden(name: str): path = _golden_path(name) if not path.exists(): pytest.fail(f"no reference data at {path}; run `python -m tests.test_logit_golden`") @@ -117,9 +151,12 @@ def test_logit_behavior_path_matches_golden(name: str): ) -def _regenerate() -> None: +def _regenerate(names: list[str]) -> None: + """Write reference data for the named cases, or for every case which has none.""" GOLDEN_DIR.mkdir(parents=True, exist_ok=True) for name, case in CASES.items(): + if (names and name not in names) or (not names and _golden_path(name).exists()): + continue data = _trace(case) # One point per line keeps the files compact and their diffs readable. lines = [ @@ -135,4 +172,4 @@ def _regenerate() -> None: if __name__ == "__main__": - _regenerate() + _regenerate(sys.argv[1:]) From 3174aaae6994d00ee6302ae1cb723f32967527d8 Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 07:42:41 +0100 Subject: [PATCH 2/8] Evaluate table game profiles from a contiguous payoff table. --- src/games/gametable.cc | 306 +++++++++++++++-------------------------- src/games/gametable.h | 19 +++ 2 files changed, 133 insertions(+), 192 deletions(-) diff --git a/src/games/gametable.cc b/src/games/gametable.cc index 9bbc14118..9a3846577 100644 --- a/src/games/gametable.cc +++ b/src/games/gametable.cc @@ -23,6 +23,7 @@ #include #include "games.h" +#include "core/lazy.h" #include "gametable.h" #include "writer.h" @@ -84,176 +85,97 @@ PureStrategyProfile GameTableRep::NewPureStrategyProfile() const std::const_pointer_cast(shared_from_this()))); } -//======================================================================== -// TableMixedStrategyProfileRep -//======================================================================== - -template class ProductDistribution { -public: - using index_type = long; - using prob_type = T; - using value_type = std::pair; - - class iterator { - public: - using iterator_category = std::forward_iterator_tag; - using difference_type = std::ptrdiff_t; - using value_type = std::pair; - using reference = value_type; - using pointer = void; - - iterator() = default; - - iterator(const SegmentedVector &probs, const SegmentedArray &offsets, size_t skip1, - size_t skip2, bool end) - : m_probs(&probs), m_offsets(&offsets), m_done(end) - { - if (m_done) { - return; - } - - const size_t P = m_probs->GetShape().size(); - - // Build active dimension list - for (size_t p = 1; p <= P; ++p) { - if (p != skip1 && p != skip2) { - m_dims.push_back(p); - } - } - - m_K = m_dims.size(); - - m_digit.assign(m_K, 0); - m_radix.assign(m_K, 0); - m_cum_prob.assign(m_K + 1, T{}); - - // initialise radices - for (size_t j = 0; j < m_K; ++j) { - const size_t p = m_dims[j]; - m_radix[j] = m_probs->segment(p).size(); - if (m_radix[j] == 0) { - m_done = true; - return; - } - } - - // initial recompute - recompute_from(0); - advance_to_next_nonzero(); +template GameTableRep::PayoffTable GameTableRep::BuildPayoffTable() const +{ + PayoffTable table(m_players.size(), std::vector(m_results.size())); + for (size_t pl = 0; pl < m_players.size(); pl++) { + const GamePlayer player = m_players[pl]; + auto &payoffs = table[pl]; + for (size_t index = 0; index < m_results.size(); index++) { + payoffs[index] = m_results[index]->GetPayoff(player); } + } + return table; +} - reference operator*() const { return {m_index, m_cum_prob[m_K]}; } - - iterator &operator++() - { - if (m_done) { - return *this; - } +template <> +std::shared_ptr> +GameTableRep::GetPayoffTable() const +{ + const std::scoped_lock lock(m_payoffTableMutex); + if (!m_doublePayoffs || m_doublePayoffsVersion != GetVersion()) { + m_doublePayoffs = std::make_shared>(BuildPayoffTable()); + m_doublePayoffsVersion = GetVersion(); + } + return m_doublePayoffs; +} - // increment odometer - size_t j = 0; - for (; j < m_K; ++j) { - if (++m_digit[j] < m_radix[j]) { - break; - } - m_digit[j] = 0; - } +template <> +std::shared_ptr> +GameTableRep::GetPayoffTable() const +{ + const std::scoped_lock lock(m_payoffTableMutex); + if (!m_rationalPayoffs || m_rationalPayoffsVersion != GetVersion()) { + m_rationalPayoffs = + std::make_shared>(BuildPayoffTable()); + m_rationalPayoffsVersion = GetVersion(); + } + return m_rationalPayoffs; +} - if (j == m_K) { - m_done = true; - return *this; - } +//======================================================================== +// TableMixedStrategyProfileRep +//======================================================================== - recompute_from(j); - advance_to_next_nonzero(); - return *this; +/// Visit each contingency of the strategies of all players other than p_skip1 and p_skip2 (player +/// numbers, or 0) which has positive probability under p_probs, calling p_visit(index, prob) with +/// its position in the table and its probability. Contingencies are visited with the strategy +/// of the lowest-numbered player varying fastest; each probability is the product of the +/// players' probabilities in order of player number. +template +void ForEachContingency(const SegmentedVector &p_probs, const SegmentedArray &p_offsets, + size_t p_skip1, size_t p_skip2, Visit p_visit) +{ + std::vector probs; + std::vector offsets; + std::vector radix; + for (size_t pl = 1; pl <= p_probs.GetShape().size(); pl++) { + if (pl == p_skip1 || pl == p_skip2) { + continue; } - - iterator operator++(int) - { - iterator tmp = *this; - ++(*this); - return tmp; + const auto segment = p_probs.segment(pl); + if (segment.empty()) { + return; } + probs.push_back(segment.data()); + offsets.push_back(p_offsets.segment(pl).data()); + radix.push_back(segment.size()); + } - bool operator==(const iterator &other) const { return m_done == other.m_done; } - - private: - void recompute_from(size_t j0) - { - m_index = 0; - m_cum_prob[0] = T{1}; - - for (size_t j = 0; j < m_K; ++j) { - const size_t p = m_dims[j]; - const size_t d = m_digit[j] + 1; - - const T pi = m_probs->segment(p)[d]; - m_cum_prob[j + 1] = m_cum_prob[j] * pi; - m_index += m_offsets->segment(p)[d]; - } + const size_t numActive = probs.size(); + std::vector digit(numActive, 0); + while (true) { + T prob{1}; + long index = 0; + for (size_t k = 0; k < numActive; k++) { + prob *= probs[k][digit[k]]; + index += offsets[k][digit[k]]; } - - void advance_to_next_nonzero() - { - while (!m_done && m_cum_prob[m_K] == T{0}) { - size_t j = 0; - for (; j < m_K; ++j) { - if (++m_digit[j] < m_radix[j]) { - break; - } - m_digit[j] = 0; - } - - if (j == m_K) { - m_done = true; - return; - } - - recompute_from(j); + if (prob != T{0}) { + p_visit(index, prob); + } + size_t k = 0; + for (; k < numActive; k++) { + if (++digit[k] < radix[k]) { + break; } + digit[k] = 0; + } + if (k == numActive) { + return; } - - const SegmentedVector *m_probs{nullptr}; - const SegmentedArray *m_offsets{nullptr}; - - std::vector m_dims; // active player numbers - size_t m_K{0}; - bool m_done{true}; - - std::vector m_digit; - std::vector m_radix; - std::vector m_cum_prob; - index_type m_index{0}; - }; - - ProductDistribution(const SegmentedVector &probs, const SegmentedArray &offsets) - : m_probs(probs), m_offsets(offsets), m_skip1(0), m_skip2(0) - { - } - - ProductDistribution(const SegmentedVector &probs, const SegmentedArray &offsets, - size_t skip1) - : m_probs(probs), m_offsets(offsets), m_skip1(skip1), m_skip2(0) - { - } - - ProductDistribution(const SegmentedVector &probs, const SegmentedArray &offsets, - size_t skip1, size_t skip2) - : m_probs(probs), m_offsets(offsets), m_skip1(skip1), m_skip2(skip2) - { } - - iterator begin() const { return iterator(m_probs, m_offsets, m_skip1, m_skip2, false); } - - iterator end() const { return iterator(m_probs, m_offsets, m_skip1, m_skip2, true); } - -private: - const SegmentedVector &m_probs; - const SegmentedArray &m_offsets; - size_t m_skip1; - size_t m_skip2; -}; +} template class TableMixedStrategyProfileRep : public MixedStrategyProfileRep { public: @@ -268,6 +190,19 @@ template class TableMixedStrategyProfileRep : public MixedStrategyProf T GetPayoffDeriv(int pl, const GameStrategy &) const override; bool GetPayoffDerivs(int pl, Vector &p_derivs) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; + +private: + Lazy>> m_payoffTable; + + /// The payoffs to player p_player (a player number) in every contingency + const std::vector &GetPayoffs(int p_player) const + { + const auto &table = m_payoffTable.Get([this] { + return dynamic_cast(*this->GetSupport().GetGame()) + .template GetPayoffTable(); + }); + return (*table)[p_player - 1]; + } }; template @@ -278,46 +213,37 @@ std::unique_ptr> TableMixedStrategyProfileRep::Cop template T TableMixedStrategyProfileRep::GetPayoff(int pl) const { - const auto game = this->GetSupport().GetGame(); - auto &g = dynamic_cast(*game); - const auto player = game->GetPlayer(pl); + const auto &payoffs = GetPayoffs(pl); T value{0}; - for (auto [index, prob] : ProductDistribution(this->m_probs, this->m_offsets)) { - value += prob * g.m_results[index]->template GetPayoff(player); - } + ForEachContingency(this->m_probs, this->m_offsets, 0, 0, + [&](long index, const T &prob) { value += prob * payoffs[index]; }); return value; } template T TableMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &strategy) const { - const auto game = this->GetSupport().GetGame(); - auto &g = dynamic_cast(*game); - auto base_index = this->StrategyOffset(strategy); - const auto player = game->GetPlayer(pl); + const auto &payoffs = GetPayoffs(pl); + const long base = this->StrategyOffset(strategy); T value{0}; - for (auto [index, prob] : ProductDistribution(this->m_probs, this->m_offsets, - strategy->GetPlayer()->GetNumber())) { - value += prob * g.m_results[base_index + index]->template GetPayoff(player); - } + ForEachContingency(this->m_probs, this->m_offsets, strategy->GetPlayer()->GetNumber(), 0, + [&](long index, const T &prob) { value += prob * payoffs[base + index]; }); return value; } template bool TableMixedStrategyProfileRep::GetPayoffDerivs(int pl, Vector &p_derivs) const { - const auto game = this->GetSupport().GetGame(); - auto &g = dynamic_cast(*game); - const auto player = game->GetPlayer(pl); + const auto &payoffs = GetPayoffs(pl); p_derivs = T{0}; - auto segment = this->m_offsets.segment(pl); - for (auto [index, prob] : ProductDistribution(this->m_probs, this->m_offsets, pl)) { - auto deriv_it = p_derivs.begin(); - for (const auto base_index : segment) { - *deriv_it += prob * g.m_results[base_index + index]->template GetPayoff(player); - ++deriv_it; - } - } + const auto segment = this->m_offsets.segment(pl); + ForEachContingency(this->m_probs, this->m_offsets, pl, 0, [&](long index, const T &prob) { + auto deriv = p_derivs.begin(); + for (const long base : segment) { + *deriv += prob * payoffs[base + index]; + ++deriv; + } + }); return true; } @@ -328,16 +254,12 @@ T TableMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &st if (strategy1->GetPlayer() == strategy2->GetPlayer()) { return T{0}; } - const auto game = this->GetSupport().GetGame(); - auto &g = dynamic_cast(*game); - auto base_index = this->StrategyOffset(strategy1) + this->StrategyOffset(strategy2); - const auto player = game->GetPlayer(pl); + const auto &payoffs = GetPayoffs(pl); + const long base = this->StrategyOffset(strategy1) + this->StrategyOffset(strategy2); T value{0}; - for (auto [index, prob] : - ProductDistribution(this->m_probs, this->m_offsets, strategy1->GetPlayer()->GetNumber(), - strategy2->GetPlayer()->GetNumber())) { - value += prob * g.m_results[base_index + index]->template GetPayoff(player); - } + ForEachContingency(this->m_probs, this->m_offsets, strategy1->GetPlayer()->GetNumber(), + strategy2->GetPlayer()->GetNumber(), + [&](long index, const T &prob) { value += prob * payoffs[base + index]; }); return value; } diff --git a/src/games/gametable.h b/src/games/gametable.h index b684c9221..05219eed8 100644 --- a/src/games/gametable.h +++ b/src/games/gametable.h @@ -23,6 +23,8 @@ #ifndef GAMBIT_GAMES_GAMETABLE_H #define GAMBIT_GAMES_GAMETABLE_H +#include + #include "gameexpl.h" namespace Gambit { @@ -35,9 +37,22 @@ class GameTableRep : public GameExplicitRep { template friend class MixedStrategyProfile; template friend class TableMixedStrategyProfileRep; +public: + /// Payoffs of every contingency, by player (indexed from 0), stored contiguously in the order + /// of the contingencies of the table + template using PayoffTable = std::vector>; + private: std::vector m_results; + // The payoff tables derived from the outcomes, and the versions of the game they describe + mutable std::mutex m_payoffTableMutex; + mutable std::shared_ptr> m_doublePayoffs; + mutable std::shared_ptr> m_rationalPayoffs; + mutable unsigned int m_doublePayoffsVersion{0}, m_rationalPayoffsVersion{0}; + + template PayoffTable BuildPayoffTable() const; + /// @name Private auxiliary functions //@{ /// Rebuild the outcome table after the strategies of p_player have changed. @@ -70,6 +85,10 @@ class GameTableRep : public GameExplicitRep { //@{ bool IsConstSum() const override; + /// Returns the payoffs of every contingency for the current version of the game, as type T + /// (double or Rational). The table is shared by all callers until the game is next modified. + template std::shared_ptr> GetPayoffTable() const; + /// Returns the smallest payoff to the player in any play of the game Rational GetPlayerMinPayoff(const GamePlayer &) const override; /// Returns the largest payoff to the player in any play of the game From 89880e972bb9b3ddf086ae78310ecd672d8f734d Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 08:41:07 +0100 Subject: [PATCH 3/8] Compute strategy payoff derivatives a player block at a time. --- src/games/gameagg.cc | 47 +++++++++++++++ src/games/gametable.cc | 89 +++++++++++++++++++++++++++ src/games/stratmixed.cc | 27 +++++++++ src/games/stratmixed.h | 21 +++++++ src/pygambit/gambit.pxd | 3 + src/pygambit/stratmixed.pxi | 10 ++++ src/pygambit/util.h | 45 ++++++++++++++ src/solvers/logit/nfglogit.cc | 96 +++++++++--------------------- tests/test_strategy_derivatives.py | 57 ++++++++++++++++++ 9 files changed, 327 insertions(+), 68 deletions(-) create mode 100644 tests/test_strategy_derivatives.py diff --git a/src/games/gameagg.cc b/src/games/gameagg.cc index 808097be9..54c7e9518 100644 --- a/src/games/gameagg.cc +++ b/src/games/gameagg.cc @@ -20,6 +20,7 @@ // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. // +#include #include #include "games.h" @@ -90,6 +91,7 @@ template class AGGMixedStrategyProfileRep : public MixedStrategyProfil T GetPayoff(int pl) const override; T GetPayoffDeriv(int pl, const GameStrategy &) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; + void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const override; }; template T AGGMixedStrategyProfileRep::GetPayoff(int pl) const @@ -168,6 +170,51 @@ T AGGMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &ps1, return g.aggPtr->getMixedPayoff(pl - 1, s); } +// Each row of derivatives comes from a single leave-one-out convolution in the AGG, which is +// available in floating point only; exact computation uses the default. +template +void AGGMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, + Matrix &p_derivs) const +{ + if constexpr (!std::is_same_v) { + MixedStrategyProfileRep::GetPayoffDerivBlock(pl, p_values, p_derivs); + } + else { + const auto game = this->m_support.GetGame(); + auto &g = dynamic_cast(*game); + const auto &agg = *g.aggPtr; + std::vector s(agg.getNumActions()); + for (int i = 0; i < agg.getNumPlayers(); ++i) { + for (int j = 0; j < agg.getNumActions(i); ++j) { + const int ind = this->m_profileIndex.at(game->GetPlayer(i + 1)->GetStrategy(j + 1)); + s[agg.firstAction(i) + j] = (ind == -1) ? 0.0 : this->m_probs.GetFlattened()[ind]; + } + } + + const auto player = game->GetPlayer(pl); + const auto &strategies = this->m_support.GetStrategies(player); + p_values = Vector(strategies.size()); + p_derivs = Matrix(strategies.size(), this->m_probs.GetFlattened().size()); + p_derivs = 0.0; + std::vector row(agg.getNumActions()); + size_t r = 1; + for (const auto &strategy : strategies) { + p_values[r] = GetPayoffDeriv(pl, strategy); + g.aggPtr->getPayoffJacobianRow(pl - 1, strategy->GetNumber() - 1, s, row); + for (const auto &other : game->GetPlayers()) { + if (other == player) { + continue; + } + for (const auto &otherStrategy : this->m_support.GetStrategies(other)) { + p_derivs(r, this->m_profileIndex.at(otherStrategy)) = + row[agg.firstAction(other->GetNumber() - 1) + otherStrategy->GetNumber() - 1]; + } + } + r++; + } + } +} + template class AGGMixedStrategyProfileRep; template class AGGMixedStrategyProfileRep; diff --git a/src/games/gametable.cc b/src/games/gametable.cc index 9a3846577..0e0dfe2f3 100644 --- a/src/games/gametable.cc +++ b/src/games/gametable.cc @@ -21,6 +21,7 @@ // #include +#include #include "games.h" #include "core/lazy.h" @@ -190,6 +191,7 @@ template class TableMixedStrategyProfileRep : public MixedStrategyProf T GetPayoffDeriv(int pl, const GameStrategy &) const override; bool GetPayoffDerivs(int pl, Vector &p_derivs) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; + void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const override; private: Lazy>> m_payoffTable; @@ -263,6 +265,93 @@ T TableMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &st return value; } +// Visits every contingency of the other players once. Each contribution is formed and +// accumulated in the same order as when the payoffs and derivatives are computed separately: +// for a derivative with respect to a strategy of player j, the probability is the product, +// in order of player number, of the probabilities of the players other than pl and j. +template +void TableMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, + Matrix &p_derivs) const +{ + const auto &payoffs = GetPayoffs(pl); + const auto &shape = this->m_probs.GetShape(); + const size_t length = this->m_probs.GetFlattened().size(); + const auto own = this->m_offsets.segment(pl); + const size_t numOwn = own.size(); + + std::vector probs; + std::vector offsets; + std::vector radix, firstColumn; + bool empty = false; + for (size_t player = 1, column = 1; player <= shape.size(); column += shape[player++]) { + if (std::cmp_equal(player, pl)) { + continue; + } + const auto segment = this->m_probs.segment(player); + empty = empty || segment.empty(); + probs.push_back(segment.data()); + offsets.push_back(this->m_offsets.segment(player).data()); + radix.push_back(segment.size()); + firstColumn.push_back(column); + } + + std::vector values(numOwn, T{0}); + std::vector derivs(numOwn * length, T{0}); // row-major, columns from 0 + const size_t numActive = probs.size(); + std::vector digit(numActive, 0); + std::vector factor(numActive); + while (!empty) { + long index = 0; + for (size_t k = 0; k < numActive; k++) { + factor[k] = probs[k][digit[k]]; + index += offsets[k][digit[k]]; + } + T prob{1}; + for (size_t k = 0; k < numActive; k++) { + prob *= factor[k]; + } + if (prob != T{0}) { + for (size_t r = 0; r < numOwn; r++) { + values[r] += prob * payoffs[own.data()[r] + index]; + } + } + for (size_t j = 0; j < numActive; j++) { + T others{1}; + for (size_t k = 0; k < numActive; k++) { + if (k != j) { + others *= factor[k]; + } + } + if (others == T{0}) { + continue; + } + const size_t column = firstColumn[j] + digit[j] - 1; + for (size_t r = 0; r < numOwn; r++) { + derivs[r * length + column] += others * payoffs[own.data()[r] + index]; + } + } + size_t k = 0; + for (; k < numActive; k++) { + if (++digit[k] < radix[k]) { + break; + } + digit[k] = 0; + } + if (k == numActive) { + break; + } + } + + p_values = Vector(numOwn); + p_derivs = Matrix(numOwn, length); + for (size_t r = 0; r < numOwn; r++) { + p_values[r + 1] = values[r]; + for (size_t c = 0; c < length; c++) { + p_derivs(r + 1, c + 1) = derivs[r * length + c]; + } + } +} + template class TableMixedStrategyProfileRep; template class TableMixedStrategyProfileRep; diff --git a/src/games/stratmixed.cc b/src/games/stratmixed.cc index 99660b9f6..a5ebae5ef 100644 --- a/src/games/stratmixed.cc +++ b/src/games/stratmixed.cc @@ -241,6 +241,33 @@ MixedStrategyProfile PureStrategyProfileRep::ToMixedStrategyProfile() return temp; } +template +void MixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, + Matrix &p_derivs) const +{ + const auto game = m_support.GetGame(); + const auto player = game->GetPlayer(pl); + const auto &strategies = m_support.GetStrategies(player); + const size_t length = m_probs.GetFlattened().size(); + p_values = Vector(strategies.size()); + p_derivs = Matrix(strategies.size(), length); + p_derivs = T{0}; + size_t row = 1; + for (const auto &strategy : strategies) { + p_values[row] = GetPayoffDeriv(pl, strategy); + size_t column = 1; + for (const auto &other : game->GetPlayers()) { + for (const auto &otherStrategy : m_support.GetStrategies(other)) { + if (other != player) { + p_derivs(row, column) = GetPayoffDeriv(pl, strategy, otherStrategy); + } + column++; + } + } + row++; + } +} + template class MixedStrategyProfileRep; template class MixedStrategyProfileRep; diff --git a/src/games/stratmixed.h b/src/games/stratmixed.h index 1eb70a23e..2cf650efb 100644 --- a/src/games/stratmixed.h +++ b/src/games/stratmixed.h @@ -26,6 +26,7 @@ #include #include +#include "core/matrix.h" #include "core/vector.h" #include "core/segment.h" #include "games/game.h" @@ -105,6 +106,10 @@ template class MixedStrategyProfileRep { virtual T GetPayoffDeriv(int pl, const GameStrategy &) const = 0; virtual bool GetPayoffDerivs(int pl, Vector &p_derivs) const { return false; } virtual T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const = 0; + /// Computes the payoffs of the strategies of player pl, and their derivatives with respect to + /// the probabilities of the strategies of the other players; see + /// MixedStrategyProfile::GetPayoffDerivBlock. The default computes each derivative separately. + virtual void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const; T GetPayoff(const GamePlayer &p_player) const { return GetPayoff(p_player->GetNumber()); } T GetPayoff(const GameStrategy &p_strategy) const @@ -311,6 +316,22 @@ template class MixedStrategyProfile { return GetPayoffDeriv(p_strategy->GetPlayer()->GetNumber(), p_strategy); } + /// @brief Computes the payoffs of a player's strategies and their derivatives + /// @details For each strategy of \p p_player in the support, computes the payoff to playing + /// it against the profile, and the derivatives of that payoff with respect to the + /// probabilities of the strategies of the other players. + /// @param[in] p_player The player whose strategies are evaluated + /// @param[out] p_values Resized to one entry per strategy of the player in the support + /// @param[out] p_derivs Resized to one row per strategy of the player in the support and one + /// column per position in the profile; columns of the player's own + /// strategies are zero + void GetPayoffDerivBlock(const GamePlayer &p_player, Vector &p_values, + Matrix &p_derivs) const + { + CheckVersion(); + m_rep->GetPayoffDerivBlock(p_player->GetNumber(), p_values, p_derivs); + } + /// @brief Computes the regret to playing \p p_strategy /// @details Computes the regret to the player of playing strategy \p p_strategy /// against the profile. The regret is defined as the difference diff --git a/src/pygambit/gambit.pxd b/src/pygambit/gambit.pxd index 001ef6ec2..1b97a2fbd 100644 --- a/src/pygambit/gambit.pxd +++ b/src/pygambit/gambit.pxd @@ -501,6 +501,9 @@ cdef extern from "util.h": stdvector[stdvector[double]] ProfileDiffActionValues( c_MixedBehaviorProfile[double] ) except + + double PayoffDerivBlockDiscrepancy( + c_MixedStrategyProfile[double], stdvector[c_GameStrategy] + ) except + void setitem_array_int "setitem"(Array[int] *, int, int) except + void setitem_array_number "setitem"(Array[c_Number], int, c_Number) except + diff --git a/src/pygambit/stratmixed.pxi b/src/pygambit/stratmixed.pxi index b082ac735..71b29a9a7 100644 --- a/src/pygambit/stratmixed.pxi +++ b/src/pygambit/stratmixed.pxi @@ -602,6 +602,16 @@ class MixedStrategyProfile: class MixedStrategyProfileDouble(MixedStrategyProfile): profile = cython.declare(shared_ptr[c_MixedStrategyProfile[double]]) + def _payoff_deriv_block_discrepancy(self, removed: list[tuple[str, str]]) -> float: + # Private, for testing: the largest discrepancy between the payoff derivative blocks of + # the players and the same quantities computed one at a time, on the support without + # the strategies `removed`, given as (player label, strategy label) pairs. + game: Game = self.game + cdef stdvector[c_GameStrategy] handles + for player, label in removed: + handles.push_back(game._resolve_strategy(player, label, "_payoff_deriv_block")) + return PayoffDerivBlockDiscrepancy(deref(self.profile), handles) + @staticmethod @cython.cfunc def wrap(profile: shared_ptr[c_MixedStrategyProfile[float]]) -> MixedStrategyProfileDouble: diff --git a/src/pygambit/util.h b/src/pygambit/util.h index 46633afad..42432e8ed 100644 --- a/src/pygambit/util.h +++ b/src/pygambit/util.h @@ -26,6 +26,8 @@ // classes easier. // +#include +#include #include #include #include @@ -133,6 +135,49 @@ ProfileDiffActionValues(const MixedBehaviorProfile &p_profile) return result; } +/// Largest absolute difference, over every player, between the payoffs and derivatives given by +/// MixedStrategyProfile::GetPayoffDerivBlock and the same quantities computed one at a time. +/// The profile checked is on the support of p_profile's game with p_removed taken out, with the +/// probabilities of the remaining strategies taken from p_profile. Private, for testing. +inline double PayoffDerivBlockDiscrepancy(const MixedStrategyProfile &p_profile, + const std::vector &p_removed) +{ + const Game game = p_profile.GetGame(); + StrategySupportProfile support(game); + for (const auto &strategy : p_removed) { + support.RemoveStrategy(strategy); + } + auto profile = support.NewMixedStrategyProfile(); + for (const auto &player : game->GetPlayers()) { + for (const auto &strategy : support.GetStrategies(player)) { + profile[strategy] = p_profile[strategy]; + } + } + double worst = 0.0; + Vector values; + Matrix derivs; + for (const auto &player : game->GetPlayers()) { + profile.GetPayoffDerivBlock(player, values, derivs); + size_t row = 1; + for (const auto &strategy : support.GetStrategies(player)) { + worst = std::max(worst, std::abs(values[row] - profile.GetPayoff(strategy))); + size_t column = 1; + for (const auto &other : game->GetPlayers()) { + for (const auto &otherStrategy : support.GetStrategies(other)) { + const double expected = + (other == player) + ? 0.0 + : profile.GetPayoffDeriv(player->GetNumber(), strategy, otherStrategy); + worst = std::max(worst, std::abs(derivs(row, column) - expected)); + column++; + } + } + row++; + } + } + return worst; +} + template std::list> make_list_of_pointer(const std::list &p_list) { std::list> result; diff --git a/src/solvers/logit/nfglogit.cc b/src/solvers/logit/nfglogit.cc index 314c2b5fd..3eda407c4 100644 --- a/src/solvers/logit/nfglogit.cc +++ b/src/solvers/logit/nfglogit.cc @@ -84,10 +84,6 @@ class Equation { virtual double Value(const MixedStrategyProfile &p_profile, const MixedStrategyProfile &p_logProfile, const Vector &p_strategyValues, double p_lambda) const = 0; - virtual void Gradient(const MixedStrategyProfile &p_profile, - const Vector &p_strategyValues, - const Matrix &p_strategyDerivs, double p_lambda, - Vector &p_gradient) const = 0; }; class SumToOneEquation final : public Equation { @@ -115,9 +111,6 @@ class SumToOneEquation final : public Equation { double Value(const MixedStrategyProfile &p_profile, const MixedStrategyProfile &p_logProfile, const Vector &p_strategyValues, double p_lambda) const override; - void Gradient(const MixedStrategyProfile &p_profile, - const Vector &p_strategyValues, const Matrix &p_strategyDerivs, - double p_lambda, Vector &p_gradient) const override; }; double SumToOneEquation::Value(const MixedStrategyProfile &p_profile, @@ -131,17 +124,6 @@ double SumToOneEquation::Value(const MixedStrategyProfile &p_profile, return value; } -void SumToOneEquation::Gradient(const MixedStrategyProfile &p_profile, - const Vector &p_strategyValues, - const Matrix &p_strategyDerivs, double p_lambda, - Vector &p_gradient) const -{ - p_gradient = 0.0; - for (int col = m_firstIndex; col < m_lastIndex; col++) { - p_gradient[col] = p_profile[col]; - } -} - class RatioEquation final : public Equation { Game m_game; GamePlayer m_player; @@ -169,9 +151,6 @@ class RatioEquation final : public Equation { double Value(const MixedStrategyProfile &p_profile, const MixedStrategyProfile &p_logProfile, const Vector &p_strategyValues, double p_lambda) const override; - void Gradient(const MixedStrategyProfile &p_profile, - const Vector &p_strategyValues, const Matrix &p_strategyDerivs, - double p_lambda, Vector &p_gradient) const override; }; double RatioEquation::Value(const MixedStrategyProfile &p_profile, @@ -182,34 +161,6 @@ double RatioEquation::Value(const MixedStrategyProfile &p_profile, p_lambda * (p_strategyValues[m_strategyIndex] - p_strategyValues[m_refStrategyIndex]); } -void RatioEquation::Gradient(const MixedStrategyProfile &p_profile, - const Vector &p_strategyValues, - const Matrix &p_strategyDerivs, double p_lambda, - Vector &p_gradient) const -{ - int col = 1; - for (const auto &player : m_game->GetPlayers()) { - for (const auto &strategy : player->GetStrategies()) { - if (strategy == m_refStrategy) { - p_gradient[col] = -1.0; - } - else if (strategy == m_strategy) { - p_gradient[col] = 1.0; - } - else if (player == m_player) { - p_gradient[col] = 0.0; - } - else { - p_gradient[col] = - -p_lambda * p_profile[col] * - (p_strategyDerivs(m_strategyIndex, col) - p_strategyDerivs(m_refStrategyIndex, col)); - } - col++; - } - } - p_gradient[col] = p_strategyValues[m_refStrategyIndex] - p_strategyValues[m_strategyIndex]; -} - class EquationSystem { public: explicit EquationSystem(const Game &p_game); @@ -223,14 +174,15 @@ class EquationSystem { Game m_game; mutable MixedStrategyProfile m_profile, m_logProfile; mutable Vector m_strategyValues; - mutable Matrix m_strategyDerivs; + // Payoffs of one player's strategies and their derivatives, reused across players + mutable Vector m_blockValues; + mutable Matrix m_blockDerivs; }; EquationSystem::EquationSystem(const Game &p_game) : m_game(p_game), m_profile(p_game->NewMixedStrategyProfile(0.0)), m_logProfile(p_game->NewMixedStrategyProfile(0.0)), - m_strategyValues(m_profile.MixedProfileLength()), - m_strategyDerivs(m_profile.MixedProfileLength(), m_profile.MixedProfileLength()) + m_strategyValues(m_profile.MixedProfileLength()) { m_equations.reserve(m_profile.MixedProfileLength()); for (const auto &player : m_game->GetPlayers()) { @@ -258,26 +210,34 @@ void EquationSystem::GetValue(const Vector &p_point, Vector &p_l void EquationSystem::GetJacobian(const Vector &p_point, Matrix &p_jac) const { + // Rows of p_jac are variables (log probabilities, then lambda); columns are equations: for + // each player, that their probabilities sum to one, then one for each strategy but the first + // relating its log probability to that of the first. PointToProfile(m_profile, p_point); const double lambda = p_point.back(); - Vector column(p_point.size()); - m_strategyDerivs = 0.0; - int row = 1; - for (const auto &strategy1 : m_game->GetStrategies()) { - m_strategyValues[row] = m_profile.GetPayoff(strategy1); - int col = 1; - for (const auto &strategy2 : m_game->GetStrategies()) { - if (strategy1->GetPlayer() != strategy2->GetPlayer()) { - m_strategyDerivs(row, col) = - m_profile.GetPayoffDeriv(strategy1->GetPlayer()->GetNumber(), strategy1, strategy2); + const size_t length = p_point.size() - 1; + p_jac = 0.0; + size_t column = 1; + size_t first = 1; // position in the profile of the current player's first strategy + for (const auto &player : m_game->GetPlayers()) { + m_profile.GetPayoffDerivBlock(player, m_blockValues, m_blockDerivs); + const size_t last = first + m_blockValues.size() - 1; + for (size_t var = first; var <= last; var++) { + p_jac(var, column) = m_profile[var]; + } + column++; + for (size_t r = 2; r <= m_blockValues.size(); r++, column++) { + for (size_t var = 1; var <= length; var++) { + if (var < first || var > last) { + p_jac(var, column) = + -lambda * m_profile[var] * (m_blockDerivs(r, var) - m_blockDerivs(1, var)); + } } - col++; + p_jac(first + r - 1, column) = 1.0; + p_jac(first, column) = -1.0; + p_jac(length + 1, column) = m_blockValues[1] - m_blockValues[r]; } - row++; - } - for (size_t i = 1; i <= m_equations.size(); i++) { - m_equations[i - 1]->Gradient(m_profile, m_strategyValues, m_strategyDerivs, lambda, column); - p_jac.SetColumn(i, column); + first = last + 1; } } diff --git a/tests/test_strategy_derivatives.py b/tests/test_strategy_derivatives.py new file mode 100644 index 000000000..6258a3423 --- /dev/null +++ b/tests/test_strategy_derivatives.py @@ -0,0 +1,57 @@ +"""Tests of MixedStrategyProfile::GetPayoffDerivBlock, which computes the payoffs of a player's +strategies and their derivatives with respect to other players' strategies together. + +The block is compared, through a private helper, with the same quantities computed one at a +time, on the full support and on supports with strategies removed. +""" +import random + +import numpy as np +import pytest + +import pygambit as gbt + +from . import games + + +def _random_table_game(shape: tuple[int, ...], seed: int) -> gbt.Game: + rng = np.random.default_rng(seed) + return gbt.StrategicGame.from_arrays(*[rng.integers(0, 100, shape) for _ in shape]) + + +def _interior_profile(game: gbt.Game, seed: int): + rng = random.Random(seed) + data = [] + for player in game.players: + weights = [rng.uniform(0.2, 1.0) for _ in game.get_strategies(player)] + data.append([w / sum(weights) for w in weights]) + return game.mixed_strategy_profile(data=data, rational=False) + + +def _removals(game: gbt.Game) -> list[list[tuple[str, str]]]: + """No removals; the first strategy of every player with more than one; and the last + strategy of the first such player only.""" + players = [p for p in game.players if len(game.get_strategies(p)) > 1] + return [ + [], + [(p, game.get_strategies(p)[0]) for p in players], + [(players[0], game.get_strategies(players[0])[-1])] if players else [], + ] + + +@pytest.mark.parametrize( + "game,tolerance", + [ + pytest.param(_random_table_game((3, 4), seed=1), 0.0, id="table-3x4"), + pytest.param(_random_table_game((3, 3, 4), seed=2), 0.0, id="table-3x3x4"), + pytest.param(_random_table_game((2, 3, 2, 3), seed=3), 0.0, id="table-2x3x2x3"), + pytest.param(games.read_from_file("2x2.agg"), 1.0e-12, id="agg-2x2"), + pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 0.0, + id="bagg-coffee"), + pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), + ], +) +def test_payoff_deriv_block_matches_separate_computation(game: gbt.Game, tolerance: float): + profile = _interior_profile(game, seed=4) + for removed in _removals(game): + assert profile._payoff_deriv_block_discrepancy(removed) <= tolerance From 986c3657be080097682bfd04144256b2a89e38c9 Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 09:14:09 +0100 Subject: [PATCH 4/8] Assemble the homotopy Jacobian from per-player payoff derivative blocks. The HP equation system's Jacobian is now filled by index from one GetPayoffDerivBlock call per player, rather than through a Gradient method on each equation that queried each derivative pairwise. The per-equation Gradient methods are removed. --- src/solvers/hp/hpsystem.cc | 89 ++++++++++++-------------------------- src/solvers/hp/hpsystem.h | 3 ++ 2 files changed, 30 insertions(+), 62 deletions(-) diff --git a/src/solvers/hp/hpsystem.cc b/src/solvers/hp/hpsystem.cc index 3f590b0b8..d704bdef9 100644 --- a/src/solvers/hp/hpsystem.cc +++ b/src/solvers/hp/hpsystem.cc @@ -33,11 +33,6 @@ class HPEquation { virtual double Value(const Vector &point, const MixedStrategyProfile ¤t_sigma, const std::vector &payoffs_against_prior) const = 0; - - virtual void Gradient(const Vector &point, - const MixedStrategyProfile ¤t_sigma, - const std::vector &payoffs_against_prior, - Vector &gradient) const = 0; }; namespace { @@ -83,46 +78,6 @@ class BestResponseEquation final : public HPEquation { return v_i + lambda - mu; } - - void Gradient(const Vector &point, const MixedStrategyProfile ¤t_sigma, - const std::vector &payoffs_against_prior, - Vector &gradient) const override - { - gradient = 0.0; - const double t = point[1]; - const GamePlayer my_player = m_strategy->GetPlayer(); - const Game game = m_strategy->GetGame(); - - // Derivative wrt t: - const double payoff_vs_sigma = current_sigma.GetPayoff(m_strategy); - const double payoff_vs_prior = payoffs_against_prior[m_flat_s_idx]; - gradient[1] = payoff_vs_sigma - payoff_vs_prior; - - // Derivative wrt mu_i: - gradient[m_mu_idx] = -1.0; - - // Derivatives wrt all alphas: - int alpha_col = 2; - for (const auto &player2 : game->GetPlayers()) { - for (const auto &strat2 : player2->GetStrategies()) { - const double alpha2 = point[alpha_col]; - - if (my_player == player2) { - if (m_strategy == strat2) { - gradient[alpha_col] = AlphaToLambdaDeriv(alpha2); - } - } - else { - // Chain rule for opposing players' strategies - const double deriv_u = - current_sigma.GetPayoffDeriv(my_player->GetNumber(), m_strategy, strat2); - const double deriv_sigma = AlphaToSigmaDeriv(alpha2); - gradient[alpha_col] = t * deriv_u * deriv_sigma; - } - alpha_col++; - } - } - } }; // Eq (b): Probability Sum Equation @@ -147,17 +102,6 @@ class ProbabilitySumEquation final : public HPEquation { } return sum_sigma - 1.0; } - - void Gradient(const Vector &point, const MixedStrategyProfile ¤t_sigma, - const std::vector &payoffs_against_prior, - Vector &gradient) const override - { - gradient = 0.0; - // Only non-zero derivatives are those with respect to the player's own alphas - for (int i = m_first_alpha_idx; i < m_last_alpha_idx; ++i) { - gradient[i] = AlphaToSigmaDeriv(point[i]); - } - } }; } // end namespace @@ -214,13 +158,34 @@ void HPEquationSystem::GetJacobian(const Vector &point, Matrix & // Update internal mutable state UpdateSigma(point); + // Rows of p_jac are variables (t, then alpha for each strategy, then mu for each player); + // columns are equations: for each player, a best response equation for each strategy, then + // that the player's probabilities sum to one. Variable 1 + k is the alpha of the strategy at + // position k of the profile. + const double t = point[1]; p_jac = 0.0; - Vector column(point.size()); // Temp vector matching Jacobian column size - - // Compute the Jacobian - for (size_t i = 1; i <= m_equations.size(); ++i) { - m_equations[i - 1]->Gradient(point, m_current_sigma, m_payoffs_against_prior, column); - p_jac.SetColumn(i, column); + size_t column = 1; + size_t first = 1; // position in the profile of the current player's first strategy + int mu_row = 2 + m_star; + for (const auto &player : m_game->GetPlayers()) { + m_current_sigma.GetPayoffDerivBlock(player, m_blockValues, m_blockDerivs); + const size_t last = first + m_blockValues.size() - 1; + for (size_t r = 1; r <= m_blockValues.size(); r++, column++) { + p_jac(1, column) = m_blockValues[r] - m_payoffs_against_prior[first + r - 2]; + for (size_t k = 1; k <= m_blockDerivs.NumColumns(); k++) { + if (k < first || k > last) { + p_jac(1 + k, column) = t * m_blockDerivs(r, k) * AlphaToSigmaDeriv(point[1 + k]); + } + } + p_jac(first + r, column) = AlphaToLambdaDeriv(point[first + r]); + p_jac(mu_row, column) = -1.0; + } + for (size_t k = first; k <= last; k++) { + p_jac(1 + k, column) = AlphaToSigmaDeriv(point[1 + k]); + } + column++; + mu_row++; + first = last + 1; } } diff --git a/src/solvers/hp/hpsystem.h b/src/solvers/hp/hpsystem.h index 3f3db28ba..c6b410a46 100644 --- a/src/solvers/hp/hpsystem.h +++ b/src/solvers/hp/hpsystem.h @@ -51,6 +51,9 @@ class HPEquationSystem { std::vector m_payoffs_against_prior; int m_star; mutable MixedStrategyProfile m_current_sigma; + // Payoffs of one player's strategies and their derivatives, reused across players + mutable Vector m_blockValues; + mutable Matrix m_blockDerivs; std::vector> m_equations; void UpdateSigma(const Vector &point) const; From 14fc484703867570f09a59600e607e3b0869df6d Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 12:42:43 +0100 Subject: [PATCH 5/8] Compute BAGG payoff derivative blocks from AGG payoff Jacobian rows. --- src/games/gamebagg.cc | 95 ++++++++++++++++++++++++++++++ tests/test_strategy_derivatives.py | 5 +- 2 files changed, 99 insertions(+), 1 deletion(-) diff --git a/src/games/gamebagg.cc b/src/games/gamebagg.cc index d202c1156..af11477ed 100644 --- a/src/games/gamebagg.cc +++ b/src/games/gamebagg.cc @@ -21,6 +21,7 @@ // #include +#include #include "games.h" #include "gamebagg.h" @@ -93,6 +94,7 @@ template class BAGGMixedStrategyProfileRep : public MixedStrategyProfi T GetPayoff(int pl) const override; T GetPayoffDeriv(int pl, const GameStrategy &) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; + void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const override; }; template T BAGGMixedStrategyProfileRep::GetPayoff(int pl) const @@ -199,6 +201,99 @@ T BAGGMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &ps1 return g.baggPtr->getMixedPayoff(bplayer, btype, s); } +// The payoff to an action of agent pl is linear in the mixed strategy each other BAGG player +// induces on its AGG actions, in which that player's type tq enters with weight P(tq). Fixing +// an action b of agent (j, tq) therefore moves the payoff by P(tq) times the difference between +// the payoff when j plays b's AGG action and its average under (j, tq)'s mixed strategy; both +// come from one row of the AGG payoff Jacobian. As with GetPayoffDeriv, derivatives with respect +// to agents of pl's own BAGG player equal the payoff, which does not depend on them. The +// Jacobian row is available in floating point only; exact computation uses the default. +template +void BAGGMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, + Matrix &p_derivs) const +{ + if constexpr (!std::is_same_v) { + MixedStrategyProfileRep::GetPayoffDerivBlock(pl, p_values, p_derivs); + } + else { + const auto game = this->m_support.GetGame(); + const auto &bagg = *dynamic_cast(*game).baggPtr; + auto &agg = *bagg.aggPtr; + const int numAgents = bagg.getNumTypes(); + + // The BAGG strategy vector, and the profile position of each of its entries (-1 if the + // strategy is not in the support); agent k's strategies start at strategyOffset[k - 1] + std::vector s(bagg.strategyOffset[numAgents]); + std::vector column(s.size()); + for (int k = 1; k <= numAgents; k++) { + int offset = bagg.strategyOffset[k - 1]; + for (const auto &strategy : game->GetPlayer(k)->GetStrategies()) { + const int ind = this->m_profileIndex.at(strategy); + s[offset] = (ind == -1) ? 0.0 : this->m_probs.GetFlattened()[ind]; + column[offset++] = ind; + } + } + + int bplayer = 0; + while (bagg.typeOffset[bplayer + 1] < pl) { + bplayer++; + } + const int btype = pl - 1 - bagg.typeOffset[bplayer]; + std::vector as(agg.getNumActions()); + bagg.getAGGStrat(as, s, bplayer, btype, 0); + const int ownFirst = agg.firstAction(bplayer); + const auto &ownActions = bagg.typeAction2ActionIndex[bplayer][btype]; + as[ownFirst + ownActions[0]] = 0.0; + + const auto &strategies = this->m_support.GetStrategies(game->GetPlayer(pl)); + p_values = Vector(strategies.size()); + p_derivs = Matrix(strategies.size(), this->m_probs.GetFlattened().size()); + p_derivs = 0.0; + std::vector row(agg.getNumActions()); + size_t r = 1; + for (const auto &strategy : strategies) { + const int action = ownActions[strategy->GetNumber() - 1]; + as[ownFirst + action] = 1.0; + const double value = agg.getV(bplayer, action, as); + p_values[r] = value; + agg.getPayoffJacobianRow(bplayer, action, as, row); + as[ownFirst + action] = 0.0; + + for (int j = 0; j < bagg.getNumPlayers(); j++) { + for (int tq = 0; tq < bagg.getNumTypes(j); tq++) { + const int agent = bagg.typeOffset[j] + tq + 1; + if (agent == pl) { + continue; + } + const int first = bagg.strategyOffset[agent - 1]; + const int count = bagg.getNumActions(j, tq); + if (j == bplayer) { + for (int b = 0; b < count; b++) { + if (column[first + b] != -1) { + p_derivs(r, column[first + b]) = value; + } + } + continue; + } + const auto &actions = bagg.typeAction2ActionIndex[j][tq]; + const double *payoffs = row.data() + agg.firstAction(j); + double mean = 0.0; + for (int b = 0; b < count; b++) { + mean += s[first + b] * payoffs[actions[b]]; + } + const double weight = bagg.indepTypeDist[j][tq]; + for (int b = 0; b < count; b++) { + if (column[first + b] != -1) { + p_derivs(r, column[first + b]) = value + weight * (payoffs[actions[b]] - mean); + } + } + } + } + r++; + } + } +} + template class BAGGMixedStrategyProfileRep; template class BAGGMixedStrategyProfileRep; diff --git a/tests/test_strategy_derivatives.py b/tests/test_strategy_derivatives.py index 6258a3423..2bfb586a5 100644 --- a/tests/test_strategy_derivatives.py +++ b/tests/test_strategy_derivatives.py @@ -46,7 +46,10 @@ def _removals(game: gbt.Game) -> list[list[tuple[str, str]]]: pytest.param(_random_table_game((3, 3, 4), seed=2), 0.0, id="table-3x3x4"), pytest.param(_random_table_game((2, 3, 2, 3), seed=3), 0.0, id="table-2x3x2x3"), pytest.param(games.read_from_file("2x2.agg"), 1.0e-12, id="agg-2x2"), - pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 0.0, + pytest.param(games.read_from_file("2x2.bagg"), 1.0e-12, id="bagg-2x2"), + pytest.param(games.read_from_file("2x2_fraction_types.bagg"), 1.0e-12, + id="bagg-2x2-fraction-types"), + pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 1.0e-12, id="bagg-coffee"), pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), ], From c4640bfd83fdbd703c94a7d588b395d44c7b7da0 Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 14:32:15 +0100 Subject: [PATCH 6/8] Return true partial derivatives of payoffs in Bayesian action-graph games. --- src/games/gamebagg.cc | 185 +++--- src/pygambit/gambit.pxd | 3 + src/pygambit/stratmixed.pxi | 5 + src/pygambit/util.h | 39 ++ .../strategy_bagg_coffee_3_2_2_3.json | 574 ++++-------------- tests/test_strategy_derivatives.py | 52 +- 6 files changed, 279 insertions(+), 579 deletions(-) diff --git a/src/games/gamebagg.cc b/src/games/gamebagg.cc index af11477ed..c54f19ed4 100644 --- a/src/games/gamebagg.cc +++ b/src/games/gamebagg.cc @@ -20,6 +20,7 @@ // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. // +#include #include #include @@ -95,6 +96,9 @@ template class BAGGMixedStrategyProfileRep : public MixedStrategyProfi T GetPayoffDeriv(int pl, const GameStrategy &) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const override; + +private: + T GetPartialDeriv(int pl, const std::vector &p_strategies) const; }; template T BAGGMixedStrategyProfileRep::GetPayoff(int pl) const @@ -121,93 +125,98 @@ template T BAGGMixedStrategyProfileRep::GetPayoff(int pl) const return g.baggPtr->getMixedPayoff(bplayer, btype, s); } +// The payoff to agent pl is linear in its own mixed strategy and in the mixed strategy each +// other BAGG player induces on its AGG actions, to which each of that player's types t +// contributes with weight P(t); it does not depend on the strategies of the other types of pl's +// own BAGG player. The partial derivative with respect to the probabilities of p_strategies is +// therefore the payoff when each is played for sure (for another BAGG player, by all of its +// types), times the probabilities of the types of the other BAGG players involved. It is zero +// if two of the strategies belong to one BAGG player, or one belongs to another type of pl's. template -T BAGGMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &ps) const +T BAGGMixedStrategyProfileRep::GetPartialDeriv( + int pl, const std::vector &p_strategies) const { - auto &g = dynamic_cast(*(this->m_support.GetGame())); - std::vector s(g.GetStrategies().size()); - int bplayer = -1, btype = -1; - for (int i = 0; i < g.baggPtr->getNumPlayers(); ++i) { - for (int tp = 0; tp < g.baggPtr->getNumTypes(i); ++tp) { - if (pl == g.baggPtr->typeOffset[i] + tp + 1) { - bplayer = i; - btype = tp; - } - if (g.baggPtr->typeOffset[i] + tp + 1 == ps->GetPlayer()->GetNumber()) { - for (unsigned int j = 0; j < g.baggPtr->typeActionSets.at(i).at(tp).size(); ++j) { - s.at(g.baggPtr->firstAction(i, tp) + j) = T(0); - } - s.at(g.baggPtr->firstAction(i, tp) + ps->GetNumber() - 1) = T(1); - } - else { - for (int j = 0; j < g.baggPtr->getNumActions(i, tp); ++j) { - const GameStrategy strategy = this->m_support.GetGame() - ->GetPlayer(g.baggPtr->typeOffset[i] + tp + 1) - ->GetStrategy(j + 1); - const int ind = this->m_profileIndex.at(strategy); - s.at(g.baggPtr->firstAction(i, tp) + j) = - (ind == -1) ? T(0) : this->m_probs.GetFlattened()[ind]; - } + const auto game = this->m_support.GetGame(); + auto &g = dynamic_cast(*game); + const auto &bagg = *g.baggPtr; + auto &agg = *bagg.aggPtr; + const int bplayer = g.agent2baggPlayer[pl] - 1; + const int btype = pl - 1 - bagg.typeOffset[bplayer]; + + int ownAction = -1; + // Each other BAGG player involved, with the AGG action it plays for sure + std::vector> fixed; + T weight(1); + for (const auto &strategy : p_strategies) { + const int agent = strategy->GetPlayer()->GetNumber(); + const int player = g.agent2baggPlayer[agent] - 1; + const int type = agent - 1 - bagg.typeOffset[player]; + if (agent == pl) { + if (ownAction != -1) { + return T(0); } + ownAction = strategy->GetNumber() - 1; + continue; + } + if (player == bplayer || std::any_of(fixed.begin(), fixed.end(), + [&](const auto &f) { return f.first == player; })) { + return T(0); + } + fixed.emplace_back(player, + agg.firstAction(player) + + bagg.typeAction2ActionIndex[player][type][strategy->GetNumber() - 1]); + if constexpr (std::is_same_v) { + weight *= static_cast(bagg.exactIndepTypeDist[player][type]); + } + else { + weight *= bagg.indepTypeDist[player][type]; } } - return g.baggPtr->getMixedPayoff(bplayer, btype, s); + + std::vector s(bagg.strategyOffset[bagg.getNumTypes()]); + for (int k = 1, offset = 0; k <= bagg.getNumTypes(); k++) { + for (const auto &strategy : game->GetPlayer(k)->GetStrategies()) { + const int ind = this->m_profileIndex.at(strategy); + s[offset++] = (ind == -1) ? T(0) : this->m_probs.GetFlattened()[ind]; + } + } + + std::vector as(agg.getNumActions()); + T value(0); + for (int action = 0; action < bagg.getNumActions(bplayer, btype); action++) { + const T prob = (ownAction == -1) ? s[bagg.firstAction(bplayer, btype) + action] + : T((action == ownAction) ? 1 : 0); + if (prob <= T(0)) { + continue; + } + bagg.getAGGStrat(as, s, bplayer, btype, action); + for (const auto &[player, index] : fixed) { + std::fill(as.begin() + agg.firstAction(player), + as.begin() + agg.firstAction(player) + agg.getNumActions(player), T(0)); + as[index] = T(1); + } + value += prob * agg.getV(bplayer, bagg.typeAction2ActionIndex[bplayer][btype][action], as); + } + return (fixed.empty()) ? value : weight * value; +} + +template +T BAGGMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &ps) const +{ + return GetPartialDeriv(pl, {ps}); } template T BAGGMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &ps1, const GameStrategy &ps2) const { - const auto player1 = ps1->GetPlayer().get(); - const auto player2 = ps2->GetPlayer().get(); - if (player1 == player2) { - return T(0); - } - - auto &g = dynamic_cast(*(this->m_support.GetGame())); - std::vector s(g.GetStrategies().size()); - int bplayer = -1, btype = -1; - for (int i = 0; i < g.baggPtr->getNumPlayers(); ++i) { - for (int tp = 0; tp < g.baggPtr->getNumTypes(i); ++tp) { - if (pl == g.baggPtr->typeOffset[i] + tp + 1) { - bplayer = i; - btype = tp; - } - - if (g.baggPtr->typeOffset[i] + tp + 1 == player1->GetNumber()) { - for (unsigned int j = 0; j < g.baggPtr->typeActionSets.at(i).at(tp).size(); ++j) { - s.at(g.baggPtr->firstAction(i, tp) + j) = T(0); - } - s.at(g.baggPtr->firstAction(i, tp) + ps1->GetNumber() - 1) = T(1); - } - else if (g.baggPtr->typeOffset[i] + tp + 1 == player2->GetNumber()) { - for (int j = 0; j < g.baggPtr->getNumActions(i, tp); ++j) { - s.at(g.baggPtr->firstAction(i, tp) + j) = T(0); - } - s.at(g.baggPtr->firstAction(i, tp) + ps2->GetNumber() - 1) = T(1); - } - else { - for (unsigned int j = 0; j < g.baggPtr->typeActionSets.at(i).at(tp).size(); ++j) { - const GameStrategy strategy = this->m_support.GetGame() - ->GetPlayer(g.baggPtr->typeOffset[i] + tp + 1) - ->GetStrategy(j + 1); - const int ind = this->m_profileIndex.at(strategy); - s.at(g.baggPtr->firstAction(i, tp) + j) = - (ind == -1) ? T(0) : this->m_probs.GetFlattened()[ind]; - } - } - } - } - return g.baggPtr->getMixedPayoff(bplayer, btype, s); + return GetPartialDeriv(pl, {ps1, ps2}); } -// The payoff to an action of agent pl is linear in the mixed strategy each other BAGG player -// induces on its AGG actions, in which that player's type tq enters with weight P(tq). Fixing -// an action b of agent (j, tq) therefore moves the payoff by P(tq) times the difference between -// the payoff when j plays b's AGG action and its average under (j, tq)'s mixed strategy; both -// come from one row of the AGG payoff Jacobian. As with GetPayoffDeriv, derivatives with respect -// to agents of pl's own BAGG player equal the payoff, which does not depend on them. The -// Jacobian row is available in floating point only; exact computation uses the default. +// See GetPartialDeriv. The derivative with respect to an action b of type tq of another BAGG +// player j is P(tq) times the payoff when j plays b's AGG action for sure, which is one entry of +// a row of the AGG payoff Jacobian. The Jacobian row is available in floating point only; exact +// computation uses the default. template void BAGGMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const @@ -260,31 +269,17 @@ void BAGGMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_va as[ownFirst + action] = 0.0; for (int j = 0; j < bagg.getNumPlayers(); j++) { + if (j == bplayer) { + continue; + } + const double *payoffs = row.data() + agg.firstAction(j); for (int tq = 0; tq < bagg.getNumTypes(j); tq++) { - const int agent = bagg.typeOffset[j] + tq + 1; - if (agent == pl) { - continue; - } - const int first = bagg.strategyOffset[agent - 1]; - const int count = bagg.getNumActions(j, tq); - if (j == bplayer) { - for (int b = 0; b < count; b++) { - if (column[first + b] != -1) { - p_derivs(r, column[first + b]) = value; - } - } - continue; - } + const int first = bagg.strategyOffset[bagg.typeOffset[j] + tq]; const auto &actions = bagg.typeAction2ActionIndex[j][tq]; - const double *payoffs = row.data() + agg.firstAction(j); - double mean = 0.0; - for (int b = 0; b < count; b++) { - mean += s[first + b] * payoffs[actions[b]]; - } const double weight = bagg.indepTypeDist[j][tq]; - for (int b = 0; b < count; b++) { + for (int b = 0; b < bagg.getNumActions(j, tq); b++) { if (column[first + b] != -1) { - p_derivs(r, column[first + b]) = value + weight * (payoffs[actions[b]] - mean); + p_derivs(r, column[first + b]) = weight * payoffs[actions[b]]; } } } diff --git a/src/pygambit/gambit.pxd b/src/pygambit/gambit.pxd index 1b97a2fbd..ca9124c15 100644 --- a/src/pygambit/gambit.pxd +++ b/src/pygambit/gambit.pxd @@ -504,6 +504,9 @@ cdef extern from "util.h": double PayoffDerivBlockDiscrepancy( c_MixedStrategyProfile[double], stdvector[c_GameStrategy] ) except + + double PayoffDerivFiniteDifferenceDiscrepancy( + c_MixedStrategyProfile[double], double + ) except + void setitem_array_int "setitem"(Array[int] *, int, int) except + void setitem_array_number "setitem"(Array[c_Number], int, c_Number) except + diff --git a/src/pygambit/stratmixed.pxi b/src/pygambit/stratmixed.pxi index 71b29a9a7..6b329e5d9 100644 --- a/src/pygambit/stratmixed.pxi +++ b/src/pygambit/stratmixed.pxi @@ -612,6 +612,11 @@ class MixedStrategyProfileDouble(MixedStrategyProfile): handles.push_back(game._resolve_strategy(player, label, "_payoff_deriv_block")) return PayoffDerivBlockDiscrepancy(deref(self.profile), handles) + def _payoff_deriv_finite_difference_discrepancy(self, step: float) -> float: + # Private, for testing: the largest discrepancy between the partial derivatives of + # payoffs and central differences of the payoffs with the given step. + return PayoffDerivFiniteDifferenceDiscrepancy(deref(self.profile), step) + @staticmethod @cython.cfunc def wrap(profile: shared_ptr[c_MixedStrategyProfile[float]]) -> MixedStrategyProfileDouble: diff --git a/src/pygambit/util.h b/src/pygambit/util.h index 42432e8ed..d9524eff0 100644 --- a/src/pygambit/util.h +++ b/src/pygambit/util.h @@ -178,6 +178,45 @@ inline double PayoffDerivBlockDiscrepancy(const MixedStrategyProfile &p_ return worst; } +/// Returns the largest discrepancy between the partial derivatives of payoffs computed by +/// GetPayoffDeriv and central differences of the payoffs, perturbing one probability at a time +/// by p_step without renormalising. Private, for testing. +inline double PayoffDerivFiniteDifferenceDiscrepancy(const MixedStrategyProfile &p_profile, + double p_step) +{ + const Game game = p_profile.GetGame(); + auto profile = p_profile; + auto difference = [&](const GameStrategy &p_wrt, auto p_payoff) { + const double prob = profile[p_wrt]; + profile[p_wrt] = prob + p_step; + const double above = p_payoff(); + profile[p_wrt] = prob - p_step; + const double below = p_payoff(); + profile[p_wrt] = prob; + return (above - below) / (2.0 * p_step); + }; + double worst = 0.0; + for (const auto &player : game->GetPlayers()) { + for (const auto &wrt : game->GetStrategies()) { + const double expected = difference(wrt, [&]() { return profile.GetPayoff(player); }); + worst = + std::max(worst, std::abs(profile.GetPayoffDeriv(player->GetNumber(), wrt) - expected)); + } + for (const auto &strategy : player->GetStrategies()) { + for (const auto &wrt : game->GetStrategies()) { + if (wrt->GetPlayer() == player) { + continue; + } + const double expected = difference(wrt, [&]() { return profile.GetPayoff(strategy); }); + worst = + std::max(worst, std::abs(profile.GetPayoffDeriv(player->GetNumber(), strategy, wrt) - + expected)); + } + } + } + return worst; +} + template std::list> make_list_of_pointer(const std::list &p_list) { std::list> result; diff --git a/tests/test_games/golden_logit/strategy_bagg_coffee_3_2_2_3.json b/tests/test_games/golden_logit/strategy_bagg_coffee_3_2_2_3.json index 7df6ab838..f5c3bb0ab 100644 --- a/tests/test_games/golden_logit/strategy_bagg_coffee_3_2_2_3.json +++ b/tests/test_games/golden_logit/strategy_bagg_coffee_3_2_2_3.json @@ -1,473 +1,111 @@ { - "counts": [{"predictor_attempts": 807, "accepted_steps": 467, "rejected_distance": 0, "rejected_contraction": 340, "rejected_orientation": 0, "corrector_iterations": 1314, "function_evals": 1314, "jacobian_evals": 808, "factorizations": 808}], + "counts": [{"predictor_attempts": 105, "accepted_steps": 105, "rejected_distance": 0, 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8.829391816417935e-85, 0.9079669435051553, 0.09203305649201407, 1.6918806828937274e-302, 8.912807925470755e-208, 2.07807899078e-312, 5.242245569372453e-139, 2.3297835674736612e-39, 1.0, 0.0, 1.6304798407041246e-66, 5.507324419534508e-248, 6.019153362664372e-28, 3.2562181431159488e-251, 8.829391816417935e-85, 0.9079669435051559, 0.09203305649201338, 1.6918806828937274e-302, 8.912807925470755e-208, 2.07807899078e-312, 5.242245569372155e-139, 2.3297835674736612e-39, 1.0, 0.0, 1.630479840703893e-66, 5.507324419535761e-248, 6.019153362664415e-28, 3.256218143116319e-251, 8.829391816417935e-85], + [10.070169104825005, 0.9083693405501666, 0.09163065944762384, 0.0, 2.1054346797203e-228, 0.0, 9.084634699369028e-153, 3.594552771988447e-43, 1.0, 0.0, 5.983653343828771e-73, 9.876615112708117e-273, 1.2172861566884522e-30, 2.760754367332342e-276, 3.7485592355671486e-93, 0.9083693405501669, 0.09163065944762352, 0.0, 2.1054346797203e-228, 0.0, 9.084634699369028e-153, 3.594552771988805e-43, 1.0, 0.0, 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2.306261117039736e-47, 1.0, 0.0, 4.9957800397927976e-80, 5.934220552134211e-300, 1.324039088276759e-33, 7.2758523596581855e-304, 2.315504745134802e-102], + [12.178032848770526, 0.9090720169906499, 0.09092798300801634, 0.0, 4.742461372926014e-276, 0.0, 1.4798772957177562e-184, 5.636271090456106e-52, 1.0, 0.0, 8.182438289974543e-88, 0.0, 7.279802775174975e-37, 0.0, 1.7161492181882205e-112, 0.9090720169906501, 0.09092798300801615, 0.0, 4.742461372926014e-276, 0.0, 1.4798772957179245e-184, 5.636271090455866e-52, 1.0, 0.0, 8.18243828997431e-88, 0.0, 7.279802775174768e-37, 0.0, 1.7161492181886108e-112, 0.9090720169906499, 0.09092798300801642, 0.0, 4.742461372926014e-276, 0.0, 1.4798772957179245e-184, 5.636271090457148e-52, 1.0, 0.0, 8.182438289976171e-88, 0.0, 7.2798027751762165e-37, 0.0, 1.7161492181886108e-112], + [13.392556821226608, 0.9093779227086107, 0.09062207729035733, 0.0, 1.6679497687817095e-303, 0.0, 7.15111131716824e-203, 4.7639762343016207e-57, 1.0, 0.0, 2.2337265064347756e-96, 0.0, 1.889797605300964e-40, 0.0, 1.2345287566008345e-123, 0.9093779227086107, 0.09062207729035729, 0.0, 1.6679497687817095e-303, 0.0, 7.151111317167833e-203, 4.7639762343021623e-57, 1.0, 0.0, 2.233726506434712e-96, 0.0, 1.8897976053012593e-40, 0.0, 1.2345287566008345e-123, 0.9093779227086111, 0.09062207729035696, 0.0, 1.667949768781899e-303, 0.0, 7.151111317168646e-203, 4.763976234301892e-57, 1.0, 0.0, 2.233726506434585e-96, 0.0, 1.8897976053012055e-40, 0.0, 1.2345287566008345e-123], + [14.728529078011167, 0.9096569306789878, 0.0903430693202158, 0.0, 0.0, 0.0, 5.093506265644792e-223, 1.2523453669042715e-62, 1.0, 0.0, 8.495632462990737e-106, 0.0, 2.1487753446996915e-44, 0.0, 6.826279352937696e-136, 0.9096569306789878, 0.09034306932021573, 0.0, 0.0, 0.0, 5.093506265645371e-223, 1.2523453669043426e-62, 1.0, 0.0, 8.49563246298977e-106, 0.0, 2.1487753447004244e-44, 0.0, 6.82627935293886e-136, 0.9096569306789878, 0.09034306932021575, 0.0, 0.0, 0.0, 5.093506265644792e-223, 1.2523453669042003e-62, 1.0, 0.0, 8.495632462990495e-106, 0.0, 2.148775344700058e-44, 0.0, 6.826279352937696e-136], + [16.198094790521147, 0.9099113342983522, 0.09008866570103442, 0.0, 0.0, 0.0, 3.507507188224689e-245, 9.110174430073964e-69, 1.0, 0.0, 3.696138687719058e-116, 0.0, 9.853501392188737e-49, 0.0, 2.2447798161480893e-149, 0.9099113342983521, 0.0900886657010345, 0.0, 0.0, 0.0, 3.507507188225088e-245, 9.110174430076035e-69, 1.0, 0.0, 3.6961386877198984e-116, 0.0, 9.853501392190978e-49, 0.0, 2.2447798161480893e-149, 0.9099113342983522, 0.0900886657010345, 0.0, 0.0, 0.0, 3.507507188225088e-245, 9.110174430076035e-69, 1.0, 0.0, 3.6961386877198984e-116, 0.0, 9.853501392190978e-49, 0.0, 2.2447798161480893e-149], + [17.81461362110428, 0.9101432433067373, 0.08985675669279142, 0.0, 0.0, 0.0, 1.468406960156387e-269, 1.61278379563649e-75, 1.0, 0.0, 1.4807964120373815e-127, 0.0, 1.6640735503459335e-53, 0.0, 3.3105315596100948e-164, 0.9101432433067377, 0.08985675669279106, 0.0, 0.0, 0.0, 1.468406960156554e-269, 1.612783795636765e-75, 1.0, 0.0, 1.4807964120372973e-127, 0.0, 1.6640735503462882e-53, 0.0, 3.3105315596108474e-164, 0.9101432433067377, 0.08985675669279101, 0.0, 0.0, 0.0, 1.468406960156554e-269, 1.6127837956367192e-75, 1.0, 0.0, 1.4807964120372973e-127, 0.0, 1.6640735503462645e-53, 0.0, 3.3105315596108474e-164], + [19.59278117375748, 0.9103545965300232, 0.08964540346961544, 0.0, 0.0, 0.0, 2.243579114987159e-296, 6.032421007671437e-83, 1.0, 0.0, 4.303560135314193e-140, 0.0, 9.36594236321522e-59, 0.0, 1.6051900169511605e-180, 0.910354596530024, 0.08964540346961465, 0.0, 0.0, 0.0, 2.243579114987159e-296, 6.032421007671437e-83, 1.0, 0.0, 4.30356013531297e-140, 0.0, 9.365942363217881e-59, 0.0, 1.6051900169516166e-180, 0.9103545965300237, 0.08964540346961489, 0.0, 0.0, 0.0, 2.243579114987159e-296, 6.032421007671437e-83, 1.0, 0.0, 4.30356013531297e-140, 0.0, 9.365942363217881e-59, 0.0, 1.6051900169511605e-180], + [21.548762589864065, 0.9105471740679978, 0.08945282593172557, 0.0, 0.0, 0.0, 0.0, 4.080887824165743e-91, 1.0, 0.0, 6.978756055485732e-154, 0.0, 1.573996923938992e-64, 0.0, 1.8186437027707314e-198, 0.9105471740679987, 0.08945282593172461, 0.0, 0.0, 0.0, 0.0, 4.080887824167367e-91, 1.0, 0.0, 6.978756055484939e-154, 0.0, 1.5739969239393055e-64, 0.0, 1.8186437027712482e-198, 0.910547174067998, 0.08945282593172534, 0.0, 0.0, 0.0, 0.0, 4.0808878241660914e-91, 1.0, 0.0, 6.978756055484939e-154, 0.0, 1.5739969239388133e-64, 0.0, 1.818643702770628e-198] ] } diff --git a/tests/test_strategy_derivatives.py b/tests/test_strategy_derivatives.py index 2bfb586a5..9cd1c8528 100644 --- a/tests/test_strategy_derivatives.py +++ b/tests/test_strategy_derivatives.py @@ -1,7 +1,8 @@ -"""Tests of MixedStrategyProfile::GetPayoffDerivBlock, which computes the payoffs of a player's -strategies and their derivatives with respect to other players' strategies together. +"""Tests of the partial derivatives of payoffs with respect to strategy probabilities. -The block is compared, through a private helper, with the same quantities computed one at a +Through private helpers, the derivatives computed one at a time are compared with central +differences of the payoffs, and MixedStrategyProfile::GetPayoffDerivBlock, which computes a +player's payoffs and derivatives together, is compared with the derivatives computed one at a time, on the full support and on supports with strategies removed. """ import random @@ -39,22 +40,41 @@ def _removals(game: gbt.Game) -> list[list[tuple[str, str]]]: ] +GAMES = [ + pytest.param(_random_table_game((3, 4), seed=1), 0.0, id="table-3x4"), + pytest.param(_random_table_game((3, 3, 4), seed=2), 0.0, id="table-3x3x4"), + pytest.param(_random_table_game((2, 3, 2, 3), seed=3), 0.0, id="table-2x3x2x3"), + pytest.param(games.read_from_file("2x2.agg"), 1.0e-12, id="agg-2x2"), + pytest.param(games.read_from_file("2x2.bagg"), 1.0e-12, id="bagg-2x2"), + pytest.param(games.read_from_file("2x2_fraction_types.bagg"), 1.0e-12, + id="bagg-2x2-fraction-types"), + pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 1.0e-12, + id="bagg-coffee"), + pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), +] + + @pytest.mark.parametrize( - "game,tolerance", + "game", [ - pytest.param(_random_table_game((3, 4), seed=1), 0.0, id="table-3x4"), - pytest.param(_random_table_game((3, 3, 4), seed=2), 0.0, id="table-3x3x4"), - pytest.param(_random_table_game((2, 3, 2, 3), seed=3), 0.0, id="table-2x3x2x3"), - pytest.param(games.read_from_file("2x2.agg"), 1.0e-12, id="agg-2x2"), - pytest.param(games.read_from_file("2x2.bagg"), 1.0e-12, id="bagg-2x2"), - pytest.param(games.read_from_file("2x2_fraction_types.bagg"), 1.0e-12, - id="bagg-2x2-fraction-types"), - pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 1.0e-12, - id="bagg-coffee"), - pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), + param if param.id != "tree-poker" else pytest.param( + param.values[0], id=param.id, + marks=pytest.mark.xfail( + strict=True, + reason="a tree's strategic payoff normalises the mixed strategy, so it is not " + "linear in each probability off the simplex", + ), + ) + for param in [pytest.param(p.values[0], id=p.id) for p in GAMES] ], ) -def test_payoff_deriv_block_matches_separate_computation(game: gbt.Game, tolerance: float): +def test_payoff_derivs_are_partial_derivatives(game: gbt.Game): + profile = _interior_profile(game, seed=4) + assert profile._payoff_deriv_finite_difference_discrepancy(1.0e-3) <= 1.0e-8 + + +@pytest.mark.parametrize("game,block_tolerance", GAMES) +def test_payoff_deriv_block_matches_separate_computation(game: gbt.Game, block_tolerance: float): profile = _interior_profile(game, seed=4) for removed in _removals(game): - assert profile._payoff_deriv_block_discrepancy(removed) <= tolerance + assert profile._payoff_deriv_block_discrepancy(removed) <= block_tolerance From ef1608f0b584d21557f508407c06b6224c2b50aa Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 15:30:24 +0100 Subject: [PATCH 7/8] Evaluate strategic-form payoffs of trees as multilinear in the probabilities. --- src/games/gametree.cc | 15 +- .../strategy_stripped_down_poker.json | 178 +++++++++--------- tests/test_qre.py | 40 ++++ tests/test_strategy_derivatives.py | 19 +- 4 files changed, 146 insertions(+), 106 deletions(-) diff --git a/src/games/gametree.cc b/src/games/gametree.cc index 639125f9c..6ff292ae7 100644 --- a/src/games/gametree.cc +++ b/src/games/gametree.cc @@ -29,6 +29,7 @@ #include #include #include +#include #include #include "games.h" @@ -61,7 +62,8 @@ std::unique_ptr> TreeMixedStrategyProfileRep::Copy template void TreeMixedStrategyProfileRep::MakeBehavior() const { if (m_mixedBehavior == nullptr) { - m_mixedBehavior = std::make_shared>(MixedStrategyProfile(Copy())); + m_mixedBehavior = + std::make_shared>(MixedStrategyProfile(this->Normalize())); } } @@ -70,10 +72,19 @@ template void TreeMixedStrategyProfileRep::OnProfileChanged() const m_mixedBehavior = nullptr; } +// The behavior profile is realization-equivalent to the normalized profile, so its payoff is +// scaled by each player's total probability. This gives the payoff as the multilinear function +// of the probabilities that the other representations compute, of which GetPayoffDeriv then +// gives the partial derivatives. template T TreeMixedStrategyProfileRep::GetPayoff(int pl) const { MakeBehavior(); - return m_mixedBehavior->GetPayoff(m_mixedBehavior->GetGame()->GetPlayer(pl)); + T payoff = m_mixedBehavior->GetPayoff(m_mixedBehavior->GetGame()->GetPlayer(pl)); + for (size_t player = 1; player <= this->m_probs.GetShape().size(); player++) { + const auto probs = std::as_const(this->m_probs).segment(player); + payoff *= std::accumulate(probs.begin(), probs.end(), static_cast(0)); + } + return payoff; } template diff --git a/tests/test_games/golden_logit/strategy_stripped_down_poker.json b/tests/test_games/golden_logit/strategy_stripped_down_poker.json index 226936419..070722e6f 100644 --- a/tests/test_games/golden_logit/strategy_stripped_down_poker.json +++ b/tests/test_games/golden_logit/strategy_stripped_down_poker.json @@ -1,94 +1,94 @@ { - "counts": [{"predictor_attempts": 88, "accepted_steps": 88, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 192, "function_evals": 192, "jacobian_evals": 89, "factorizations": 89}], + "counts": [{"predictor_attempts": 88, "accepted_steps": 88, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 166, "function_evals": 166, "jacobian_evals": 89, "factorizations": 89}], "points": [ [0.0, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5], - [0.018087976768584875, 0.25339258279875193, 0.25226476875477755, 0.24772261313447003, 0.24662003531227308, 0.5022557548917644, 0.4977442451053195], - [0.03797854470500962, 0.25712484325092405, 0.2547636352152455, 0.24518152633484178, 0.24292999519976274, 0.5047235863497112, 0.49527641364034486], - [0.05984835435308084, 0.2612286342171476, 0.25752069365033226, 0.24234528903314698, 0.23890538310141207, 0.5074204448521542, 0.49257955512288587], - 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1.630474945419809e-104, 0.6692077067403387, 0.3307922932596993], + [196.6345716615844, 0.33571872957362997, 0.6642812704263349, 3.6652549877031296e-115, 7.252381309675541e-115, 0.6689803729460543, 0.3310196270539747], + [216.29931631640073, 0.3354989774876767, 0.6645010225122971, 1.5018400990703435e-126, 2.974597088060666e-126, 0.6687730610830636, 0.3312269389169584], + [237.930590715992, 0.3352996993775376, 0.6647003006224428, 4.4714196232023166e-139, 8.864171286968723e-139, 0.6685840648018677, 0.3314159351981488], + [261.7250426871568, 0.33511894982217255, 0.6648810507838461, 7.442089867277538e-153, 1.4765218539891208e-152, 0.668411812827512, 0.3315881877045806], + [287.898985325686, 0.3349549732831252, 0.6650450272149685, 5.189322486326558e-168, 1.0303274736658818e-167, 0.6682548595913906, 0.3317451408511756], + [316.6903634798237, 0.33480618698849623, 0.6651938134210938, 1.1038382973183169e-184, 2.1931088340927757e-184, 0.6681118778594762, 0.3318881225083867], + [348.36091687966353, 0.33467116151769005, 0.6653288388192639, 5.0525861008532416e-203, 1.0044579964017001e-202, 0.6679816496634652, 0.33201835064213486], + [383.1985595876543, 0.33454860564254346, 0.6654513946347641, 3.390108901440652e-223, 6.7432733491583815e-223, 0.6678630585514908, 0.33213694170225777], + [421.51999739720463, 0.33443735237647637, 0.6655626478518253, 2.1858056618168894e-245, 4.349964481033075e-245, 0.6677550819949988, 0.33224491821560126], + [463.6736069746099, 0.3343363465218644, 0.6656636536661539, 8.510883073799361e-270, 1.6945167887873223e-269, 0.6676567841929227, 0.33234321598179517], + [510.04260291827063, 0.33424463354227835, 0.6657553666126116, 1.2005964502467616e-296, 2.391372814028285e-296, 0.6675673092900798, 0.33243269085481675], + [561.0485215266102, 0.3341613496077681, 0.6658386505198661, 0.0, 0.0, 0.6674858750154454, 0.3325141251046804], + [617.1550529452727, 0.33408571268007337, 0.6659142874251283, 0.0, 0.0, 0.6674117667375344, 0.3325882333620259] ] } diff --git a/tests/test_qre.py b/tests/test_qre.py index e5d7294e5..cc3ff2b8d 100644 --- a/tests/test_qre.py +++ b/tests/test_qre.py @@ -1,3 +1,6 @@ +import io + +import numpy as np import pytest import pygambit as gbt @@ -80,3 +83,40 @@ def test_logit_estimate_behavior_completes(use_empirical: bool, local_max: bool) probs = dict(result.profile[selector]) assert probs.keys() == set(data.game.get_actions(selector)) assert sum(probs.values()) == pytest.approx(1.0) + + +def _logit_strategy_path(game: gbt.Game, lam: float) -> tuple[np.ndarray, list[tuple[int, int]]]: + events = [] + _, stats = gbt.gambit._logit_strategy_lambda(game, [lam], 0.03, 1.1, events.append, + _with_stats=True) + points = np.array([ + [event.qre.lam] + [event.qre[i] for i in range(len(event.qre))] + for event in events if isinstance(event, gbt.LogitPathEvent) + ]) + return points, [(s.accepted_steps, s.corrector_iterations) for s in stats] + + +@pytest.mark.parametrize( + "game", + [ + pytest.param(games.create_stripped_down_poker_efg(), id="stripped_down_poker"), + pytest.param(games.create_stripped_down_poker_efg(nonterm_outcomes=True), + id="stripped_down_poker_nonterm_outcomes"), + pytest.param(games.read_from_file("3_player_with_nonterm_outcomes.efg"), + id="3_player_with_nonterm_outcomes"), + pytest.param(games.read_from_file("chance_in_middle_with_nonterm_outcomes.efg"), + id="chance_in_middle_with_nonterm_outcomes"), + pytest.param(games.read_from_file("nature_leaves_generic.efg"), + id="nature_leaves_generic"), + ], +) +def test_logit_strategy_tree_matches_table_form(game: gbt.Game): + """Strategic-form logit on a tree traces the same path as on the table game written from + its reduced strategic form. A fixed lambda is used so the comparison does not depend on + the payoff range, which is defined differently for the two representations.""" + table = gbt.read_nfg(io.BytesIO(game.to_nfg().encode())) + tree_points, tree_counts = _logit_strategy_path(game, 5.0) + table_points, table_counts = _logit_strategy_path(table, 5.0) + assert tree_counts == table_counts + assert tree_points.shape == table_points.shape + assert np.max(np.abs(tree_points - table_points)) <= 1.0e-12 diff --git a/tests/test_strategy_derivatives.py b/tests/test_strategy_derivatives.py index 9cd1c8528..324e2002a 100644 --- a/tests/test_strategy_derivatives.py +++ b/tests/test_strategy_derivatives.py @@ -51,24 +51,13 @@ def _removals(game: gbt.Game) -> list[list[tuple[str, str]]]: pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 1.0e-12, id="bagg-coffee"), pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), + pytest.param(games.read_from_file("chance_in_middle_with_nonterm_outcomes.efg"), 0.0, + id="tree-chance-in-middle"), ] -@pytest.mark.parametrize( - "game", - [ - param if param.id != "tree-poker" else pytest.param( - param.values[0], id=param.id, - marks=pytest.mark.xfail( - strict=True, - reason="a tree's strategic payoff normalises the mixed strategy, so it is not " - "linear in each probability off the simplex", - ), - ) - for param in [pytest.param(p.values[0], id=p.id) for p in GAMES] - ], -) -def test_payoff_derivs_are_partial_derivatives(game: gbt.Game): +@pytest.mark.parametrize("game,block_tolerance", GAMES) +def test_payoff_derivs_are_partial_derivatives(game: gbt.Game, block_tolerance: float): profile = _interior_profile(game, seed=4) assert profile._payoff_deriv_finite_difference_discrepancy(1.0e-3) <= 1.0e-8 From 8bc93b36036363230f75e77804864bf60f1dd8ef Mon Sep 17 00:00:00 2001 From: Theodore Turocy Date: Tue, 29 Sep 2026 15:53:06 +0100 Subject: [PATCH 8/8] Compute strategic-form payoff derivatives of trees from the tree. --- src/games/game.h | 1 + src/games/gametree.cc | 178 +++++++++++++++++++++++++++++ src/games/gametree.h | 4 + tests/test_strategy_derivatives.py | 4 +- 4 files changed, 185 insertions(+), 2 deletions(-) diff --git a/src/games/game.h b/src/games/game.h index 39629fed6..b9d174c73 100644 --- a/src/games/game.h +++ b/src/games/game.h @@ -402,6 +402,7 @@ class GameStrategyRep : public std::enable_shared_from_this { template friend class MixedStrategyProfile; template friend class TableMixedStrategyProfileRep; template friend class MixedBehaviorProfile; + friend struct TreeSequenceLayout; bool m_valid{true}; GamePlayerRep *m_player; diff --git a/src/games/gametree.cc b/src/games/gametree.cc index 6ff292ae7..7bb4bc2f6 100644 --- a/src/games/gametree.cc +++ b/src/games/gametree.cc @@ -108,6 +108,184 @@ T TreeMixedStrategyProfileRep::GetPayoffDeriv(int pl, const GameStrategy &str return tmp.GetPayoff(pl); } +/// The sequence of each player at each node of a tree with perfect recall, and the sequences each +/// reduced strategy is consistent with. A player's sequence at a node is the player's last action +/// on the path to it, numbered from 1 among that player's actions in the order of the +/// TreeLayout; 0 is the empty sequence. A strategy is consistent with the empty sequence and with +/// each action it chooses. +struct TreeSequenceLayout { + std::shared_ptr tree; + bool perfectRecall; + std::vector numSequences; ///< by player + std::vector nodeSequences; ///< numPlayers per node + /// by player, then strategy in the order of GamePlayerRep::GetStrategies() + std::vector>> strategySequences; + + explicit TreeSequenceLayout(const GameRep &p_game) + : tree(p_game.GetTreeLayout()), perfectRecall(p_game.IsPerfectRecall()), + numSequences(tree->numPlayers, 1) + { + if (!perfectRecall) { + return; + } + const size_t numPlayers = tree->numPlayers; + std::vector sequenceOfAction(tree->numActions + 1, 0); + std::vector playerOfAction(tree->numActions + 1, -1); + for (size_t i = 0; i < tree->numPersonalInfosets; i++) { + const auto &infoset = tree->infosets[i]; + for (size_t a = 0; a < infoset.numActions; a++) { + playerOfAction[infoset.firstAction + a] = infoset.player; + sequenceOfAction[infoset.firstAction + a] = numSequences[infoset.player]++; + } + } + nodeSequences.resize(tree->parent.size() * numPlayers, 0); + for (size_t node = 1; node < tree->parent.size(); node++) { + std::copy_n(nodeSequences.begin() + tree->parent[node] * numPlayers, numPlayers, + nodeSequences.begin() + node * numPlayers); + if (const size_t action = tree->action[node]; action != 0) { + nodeSequences[node * numPlayers + playerOfAction[action]] = sequenceOfAction[action]; + } + } + for (const auto &player : p_game.GetPlayers()) { + auto &sequences = strategySequences.emplace_back(); + for (const auto &strategy : player->GetStrategies()) { + auto &consistent = sequences.emplace_back(1, 0); + for (const auto &[infoset, action] : strategy->m_behav) { + if (action > 0) { + consistent.push_back( + sequenceOfAction[tree->infosets[tree->infosetIndex.at(infoset)].firstAction + + action - 1]); + } + } + } + } + } +}; + +// The payoff is the sum over nodes of the probability chance leads to the node, times the payoff +// of the outcome there, times the probability of each player's sequence at the node, which is the +// total probability of the strategies consistent with it. The payoff to a strategy s of player +// i, and its derivative with respect to the probability of a strategy t of player j, therefore +// sum, over the sequences of i consistent with s (and of j consistent with t), quantities +// accumulated over the nodes where those are the players' sequences. +template +void TreeMixedStrategyProfileRep::GetPayoffDerivBlock(int pl, Vector &p_values, + Matrix &p_derivs) const +{ + const auto game = this->m_support.GetGame(); + if (!m_sequences || m_sequences->tree != game->GetTreeLayout()) { + m_sequences = std::make_shared(*game); + } + const auto &layout = *m_sequences; + if (!layout.perfectRecall) { + MixedStrategyProfileRep::GetPayoffDerivBlock(pl, p_values, p_derivs); + return; + } + const auto &tree = *layout.tree; + const auto &numbers = tree.template GetNumbers(); + const size_t numPlayers = tree.numPlayers; + const size_t numNodes = tree.parent.size(); + const size_t self = pl - 1; + + // Probability of each sequence of each player + std::vector> seqProbs(numPlayers); + for (size_t k = 0; k < numPlayers; k++) { + seqProbs[k].assign(layout.numSequences[k], static_cast(0)); + const auto player = game->GetPlayer(k + 1); + for (const auto &strategy : this->m_support.GetStrategies(player)) { + const T &prob = this->m_probs.GetFlattened()[this->m_profileIndex.at(strategy)]; + for (const size_t sequence : layout.strategySequences[k][strategy->GetNumber() - 1]) { + seqProbs[k][sequence] += prob; + } + } + } + + // Accumulate over nodes, by the sequence of the player (values) and by the sequences of the + // player and of each other player (derivatives) + const size_t numOwn = layout.numSequences[self]; + std::vector ownValues(numOwn, static_cast(0)); + std::vector> pairValues(numPlayers); + for (size_t j = 0; j < numPlayers; j++) { + if (j != self) { + pairValues[j].assign(numOwn * layout.numSequences[j], static_cast(0)); + } + } + std::vector chance(numNodes); + for (size_t node = 0; node < numNodes; node++) { + chance[node] = + (node == 0) ? numbers.chanceProb[0] : chance[tree.parent[node]] * numbers.chanceProb[node]; + const T &payoff = numbers.payoffs[node * numPlayers + self]; + if (payoff == static_cast(0) || chance[node] == static_cast(0)) { + continue; + } + const size_t *sequences = layout.nodeSequences.data() + node * numPlayers; + const T base = chance[node] * payoff; + T all = base; + for (size_t k = 0; k < numPlayers; k++) { + if (k != self) { + all *= seqProbs[k][sequences[k]]; + } + } + ownValues[sequences[self]] += all; + for (size_t j = 0; j < numPlayers; j++) { + if (j == self) { + continue; + } + T others = base; + for (size_t k = 0; k < numPlayers; k++) { + if (k != self && k != j) { + others *= seqProbs[k][sequences[k]]; + } + } + pairValues[j][sequences[self] * layout.numSequences[j] + sequences[j]] += others; + } + } + + const auto player = game->GetPlayer(pl); + const auto &strategies = this->m_support.GetStrategies(player); + const auto &ownSequences = layout.strategySequences[self]; + p_values = Vector(strategies.size()); + p_derivs = Matrix(strategies.size(), this->m_probs.GetFlattened().size()); + p_derivs = static_cast(0); + size_t row = 1; + for (const auto &strategy : strategies) { + T value = static_cast(0); + for (const size_t sequence : ownSequences[strategy->GetNumber() - 1]) { + value += ownValues[sequence]; + } + p_values[row++] = value; + } + + // For each strategy t of another player j, sum over t's sequences for each sequence of the + // player, then over each of the player's strategies' sequences + std::vector byOwnSequence(numOwn); + for (size_t j = 0; j < numPlayers; j++) { + if (j == self) { + continue; + } + const size_t numOther = layout.numSequences[j]; + for (const auto &other : this->m_support.GetStrategies(game->GetPlayer(j + 1))) { + const auto &otherSequences = layout.strategySequences[j][other->GetNumber() - 1]; + for (size_t q = 0; q < numOwn; q++) { + T sum = static_cast(0); + for (const size_t sequence : otherSequences) { + sum += pairValues[j][q * numOther + sequence]; + } + byOwnSequence[q] = sum; + } + const int column = this->m_profileIndex.at(other); + row = 1; + for (const auto &strategy : strategies) { + T deriv = static_cast(0); + for (const size_t sequence : ownSequences[strategy->GetNumber() - 1]) { + deriv += byOwnSequence[sequence]; + } + p_derivs(row++, column) = deriv; + } + } + } +} + template class TreeMixedStrategyProfileRep; template class TreeMixedStrategyProfileRep; diff --git a/src/games/gametree.h b/src/games/gametree.h index 89f825638..1f41111ee 100644 --- a/src/games/gametree.h +++ b/src/games/gametree.h @@ -889,6 +889,8 @@ class GameTreeRep final : public GameExplicitRep { const std::vector &); }; +struct TreeSequenceLayout; + template class TreeMixedStrategyProfileRep : public MixedStrategyProfileRep { public: explicit TreeMixedStrategyProfileRep(const StrategySupportProfile &p_support) @@ -902,9 +904,11 @@ template class TreeMixedStrategyProfileRep : public MixedStrategyProfi T GetPayoff(int pl) const override; T GetPayoffDeriv(int pl, const GameStrategy &) const override; T GetPayoffDeriv(int pl, const GameStrategy &, const GameStrategy &) const override; + void GetPayoffDerivBlock(int pl, Vector &p_values, Matrix &p_derivs) const override; private: mutable std::shared_ptr> m_mixedBehavior; + mutable std::shared_ptr m_sequences; void MakeBehavior() const; void OnProfileChanged() const override; diff --git a/tests/test_strategy_derivatives.py b/tests/test_strategy_derivatives.py index 324e2002a..16cad71b7 100644 --- a/tests/test_strategy_derivatives.py +++ b/tests/test_strategy_derivatives.py @@ -50,8 +50,8 @@ def _removals(game: gbt.Game) -> list[list[tuple[str, str]]]: id="bagg-2x2-fraction-types"), pytest.param(games.read_from_file("Bayesian-Coffee-3-2-2-3.bagg"), 1.0e-12, id="bagg-coffee"), - pytest.param(games.create_stripped_down_poker_efg(), 0.0, id="tree-poker"), - pytest.param(games.read_from_file("chance_in_middle_with_nonterm_outcomes.efg"), 0.0, + pytest.param(games.create_stripped_down_poker_efg(), 1.0e-12, id="tree-poker"), + pytest.param(games.read_from_file("chance_in_middle_with_nonterm_outcomes.efg"), 1.0e-12, id="tree-chance-in-middle"), ]