diff --git a/ChangeLog b/ChangeLog index 0fda659d47..562fe7122c 100644 --- a/ChangeLog +++ b/ChangeLog @@ -24,6 +24,10 @@ and of payoffs, beliefs and regrets of mixed behavior profiles on large game trees. Path following (logit and hp) also spends about half as long factorizing Jacobians. (#1162) +### Fixed +- `maxregret` is now scaled by the range of feasible expected payoffs, so the tolerance no longer + depends on whether a game is represented as a tree or as a table. (#1168) + ## [17.0.0-beta.1] - 2026-09-08 ### Added diff --git a/doc/algorithms.rst b/doc/algorithms.rst index db71bc87d2..8fcf921e93 100644 --- a/doc/algorithms.rst +++ b/doc/algorithms.rst @@ -38,9 +38,9 @@ deviating. Every Nash equilibrium is an :math:`\varepsilon`-equilibrium with To provide a uniform interface across methods, where relevant Gambit provides a parameter `maxregret`, which specifies the acceptance criterion for labeling the output of the algorithm as an equilibrium. This parameter is interpreted *proportionally* to the range of -payoffs in the game: any profile returned as an equilibrium is guaranteed to be an +expected payoffs in the game: any profile returned as an equilibrium is guaranteed to be an :math:`\varepsilon`-equilibrium, for :math:`\varepsilon` no more than `maxregret` times the -difference of the game's maximum and minimum payoffs. For example, with the default +difference of the game's maximum and minimum expected payoffs. For example, with the default `maxregret` of :math:`10^{-8}` in a game whose payoffs range over 4 units, any equilibrium returned is guaranteed to have a regret, measured directly in the game's own payoffs, of no more than :math:`4 \times 10^{-8}`. diff --git a/doc/tools.liap.rst b/doc/tools.liap.rst index 62575ca6d0..15f3ecb639 100644 --- a/doc/tools.liap.rst +++ b/doc/tools.liap.rst @@ -16,7 +16,7 @@ See the :ref:`algorithm description ` for full details. The criterion for accepting whether a local constrained minimizer of the Lyanunov function is an approximate Nash equilibrium is specified in terms of the maximum regret. This regret is interpreted as a fraction - of the difference between the maximum and minimum payoffs in the game. + of the difference between the maximum and minimum expected payoffs in the game. .. versionchanged:: 16.5.0 diff --git a/doc/tools.logit.rst b/doc/tools.logit.rst index 521b7bef4f..bd4eee9e10 100644 --- a/doc/tools.logit.rst +++ b/doc/tools.logit.rst @@ -11,7 +11,7 @@ See the :ref:`algorithm description ` for full details. The criterion for accepting whether a point is sufficiently close to a Nash equilibrium to terminate the path-following is specified in terms of the maximum regret. This regret is interpreted as a fraction - of the difference between the maximum and minimum payoffs in the game. + of the difference between the maximum and minimum expected payoffs in the game. .. program:: gambit-logit diff --git a/src/games/game.cc b/src/games/game.cc index b6c7dfdd23..5a28e63657 100644 --- a/src/games/game.cc +++ b/src/games/game.cc @@ -174,6 +174,36 @@ GameRep::~GameRep() m_nullOutcome->Invalidate(); } +std::pair +GameRep::GetPlayerExpectedPayoffRange(const GamePlayer &p_player) const +{ + const Rational first = NewPureStrategyProfile()->GetPayoff(p_player); + std::pair range{first, first}; + for (const auto &profile : + StrategyContingencies(std::const_pointer_cast(shared_from_this()))) { + const Rational payoff = profile->GetPayoff(p_player); + range.first = std::min(range.first, payoff); + range.second = std::max(range.second, payoff); + } + return range; +} + +std::pair GameRep::GetExpectedPayoffRange() const +{ + const Rational first = + NewPureStrategyProfile()->GetPayoff(m_players.front()->shared_from_this()); + std::pair range{first, first}; + for (const auto &profile : + StrategyContingencies(std::const_pointer_cast(shared_from_this()))) { + for (const auto &player : m_players) { + const Rational payoff = profile->GetPayoff(player->shared_from_this()); + range.first = std::min(range.first, payoff); + range.second = std::max(range.second, payoff); + } + } + return range; +} + void GameRep::IndexStrategies() const { const size_t n = m_players.size(); diff --git a/src/games/game.h b/src/games/game.h index b9d174c730..c633d167d2 100644 --- a/src/games/game.h +++ b/src/games/game.h @@ -733,6 +733,22 @@ class GameRep : public std::enable_shared_from_this { /// Returns the largest payoff to the player in any play of the game virtual Rational GetPlayerMaxPayoff(const GamePlayer &p_player) const = 0; + /// Returns the (minimum, maximum) expected payoff to the player over all pure strategy profiles + /// (that is, over the cells of the reduced strategic form). + /// @throws UndefinedException if the game has absent-mindedness + virtual std::pair + GetPlayerExpectedPayoffRange(const GamePlayer &p_player) const; + /// Returns the (minimum, maximum) expected payoff to any player over all pure strategy profiles + /// @throws UndefinedException if the game has absent-mindedness + virtual std::pair GetExpectedPayoffRange() const; + /// Returns the (minimum, maximum) expected payoff to any player over all pure behavior profiles, + /// that is, over the pure strategy profiles of the agent form. Games with no distinct agent + /// form report the same range as GetExpectedPayoffRange(). + virtual std::pair GetAgentExpectedPayoffRange() const + { + return GetExpectedPayoffRange(); + } + /// Returns the set of terminal nodes which are descendants of node virtual std::vector GetPlays(GameNode node) const { throw UndefinedException(); } /// Returns the set of terminal nodes which are descendants of members of an infoset diff --git a/src/games/gametree.cc b/src/games/gametree.cc index b43c1e9d6a..abf4a6b6bc 100644 --- a/src/games/gametree.cc +++ b/src/games/gametree.cc @@ -23,8 +23,11 @@ #include #include #include +#include #include #include +#include +#include #include #include #include @@ -1266,6 +1269,108 @@ Rational GameTreeRep::GetPlayerMaxPayoff(const GamePlayer &p_player) const }); } +namespace { + +// Enumerates pure behavior profiles lazily, branching on an information set only when the walk +// first reaches it. Profiles that agree on every information set they reach have the same +// payoffs, so each such class is visited once. +class PureBehaviorRangeScanner { + using Pending = std::vector>; + + std::vector m_players; + std::map m_assigned; + std::vector>> m_ranges; + + void Explore(Pending p_pending, std::vector p_totals) + { + while (!p_pending.empty()) { + const auto [node, weight] = p_pending.back(); + p_pending.pop_back(); + for (size_t pl = 0; pl < m_players.size(); pl++) { + p_totals[pl] += weight * node->GetOutcome()->GetPayoff(m_players[pl]); + } + if (node->IsTerminal()) { + continue; + } + const GameInfoset infoset = node->GetInfoset(); + if (infoset->IsChanceInfoset()) { + for (const auto &action : infoset->GetActions()) { + p_pending.emplace_back( + node->GetChild(action), + weight * static_cast(infoset->GetActionProb(action))); + } + } + else if (const auto assigned = m_assigned.find(infoset); assigned != m_assigned.end()) { + p_pending.emplace_back(node->GetChild(assigned->second), weight); + } + else { + for (const auto &action : infoset->GetActions()) { + m_assigned[infoset] = action; + Pending branch = p_pending; + branch.emplace_back(node->GetChild(action), weight); + Explore(std::move(branch), p_totals); + } + m_assigned.erase(infoset); + return; + } + } + for (size_t pl = 0; pl < m_players.size(); pl++) { + auto &range = m_ranges[pl]; + range = range ? std::pair{std::min(range->first, p_totals[pl]), + std::max(range->second, p_totals[pl])} + : std::pair{p_totals[pl], p_totals[pl]}; + } + } + +public: + explicit PureBehaviorRangeScanner(const Game &p_game) + : m_players(p_game->GetPlayers().begin(), p_game->GetPlayers().end()), + m_ranges(m_players.size()) + { + } + + std::vector> Scan(const GameNode &p_root) + { + Explore({{p_root, Rational(1)}}, std::vector(m_players.size(), Rational(0))); + std::vector> result; + std::transform(m_ranges.begin(), m_ranges.end(), std::back_inserter(result), + [](const auto &range) { return *range; }); + return result; + } +}; + +} // end anonymous namespace + +std::vector> GameTreeRep::ScanExpectedPayoffRanges() const +{ + if (!GetAbsentMindedReentries().empty()) { + throw UndefinedException( + "Expected payoff ranges are not defined for games with absent-mindedness."); + } + const Game game(const_cast(this)->shared_from_this()); + return PureBehaviorRangeScanner(game).Scan(m_root); +} + +std::pair +GameTreeRep::GetPlayerExpectedPayoffRange(const GamePlayer &p_player) const +{ + if (p_player->GetGame().get() != this) { + throw MismatchException(); + } + return ScanExpectedPayoffRanges().at(p_player->GetNumber() - 1); +} + +std::pair GameTreeRep::GetExpectedPayoffRange() const +{ + const auto ranges = ScanExpectedPayoffRanges(); + return {std::min_element(ranges.begin(), ranges.end(), + [](const auto &a, const auto &b) { return a.first < b.first; }) + ->first, + std::max_element(ranges.begin(), ranges.end(), [](const auto &a, const auto &b) { + return a.second < b.second; + })->second}; +} + bool GameTreeRep::IsPerfectRecall() const { EnsureOwnPriorActions(); diff --git a/src/games/gametree.h b/src/games/gametree.h index 1ac5d8a670..05a78406f2 100644 --- a/src/games/gametree.h +++ b/src/games/gametree.h @@ -739,6 +739,7 @@ class GameTreeRep final : public GameExplicitRep { /// @name Private auxiliary functions //@{ static void SortInfosets(GamePlayerRep *); + std::vector> ScanExpectedPayoffRanges() const; template Rational AggregateSubtreePayoff(const GamePlayer &p_player, Aggregator p_aggregator) const; static void RenumberInfosets(GamePlayerRep *); @@ -791,6 +792,8 @@ class GameTreeRep final : public GameExplicitRep { Rational GetPlayerMinPayoff(const GamePlayer &) const override; /// Returns the largest payoff to the player in any play of the game Rational GetPlayerMaxPayoff(const GamePlayer &) const override; + std::pair GetPlayerExpectedPayoffRange(const GamePlayer &) const override; + std::pair GetExpectedPayoffRange() const override; bool IsAbsentMinded(const GameInfoset &p_infoset) const override; std::vector> GetAbsentMindedReentries() const override; std::shared_ptr GetTreeLayout() const override; diff --git a/src/pygambit/nash.py b/src/pygambit/nash.py index b46a4bc58d..b0b859bccb 100644 --- a/src/pygambit/nash.py +++ b/src/pygambit/nash.py @@ -424,7 +424,7 @@ def liap_solve( maxregret : float, default 1e-4 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game .. versionadded:: 16.2.0 @@ -491,7 +491,7 @@ def liap_agent_solve( maxregret : float, default 1e-4 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game maxiter : int, default 1000 Maximum number of iterations in function minimization. @@ -548,7 +548,7 @@ def simpdiv_solve( maxregret : Rational, default 1e-7 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game .. versionadded:: 16.2.0 @@ -824,7 +824,7 @@ def enumpoly_solve( maxregret : float, default 1e-8 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game max_rectangles : int, default 20000 The maximum number of rectangles to examine when searching for equilibria on a @@ -947,7 +947,7 @@ def logit_solve( maxregret : float, default 1e-8 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game .. versionadded:: 16.2.0 @@ -1007,7 +1007,7 @@ def hp_solve( maxregret : float, default 1e-8 The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than `maxregret` times the - difference of the maximum and minimum payoffs of the game + difference of the maximum and minimum expected payoffs of the game event_callback : Callable[[HPStepEvent], None], optional If specified, called with each point traced along the homotopy path, diff --git a/src/solvers/enummixed/enummixed.cc b/src/solvers/enummixed/enummixed.cc index 0f5b2671a8..a931493774 100644 --- a/src/solvers/enummixed/enummixed.cc +++ b/src/solvers/enummixed/enummixed.cc @@ -85,10 +85,7 @@ EnumMixedStrategySolveDetailed(const Game &p_game, StrategyCallbackType p_onE if (p_game->NumPlayers() != 2) { throw UndefinedException("Method only valid for two-player games."); } - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); std::shared_ptr> solution(new EnumMixedStrategySolution(p_game)); const PureStrategyProfile profile = p_game->NewPureStrategyProfile(); diff --git a/src/solvers/enumpoly/efgpoly.cc b/src/solvers/enumpoly/efgpoly.cc index 26d9754b2f..1453560ed1 100644 --- a/src/solvers/enumpoly/efgpoly.cc +++ b/src/solvers/enumpoly/efgpoly.cc @@ -234,15 +234,9 @@ EnumPolyBehaviorSolve(const Game &p_game, std::optional p_stopAfter, dou EnumPolyEventCallbackType p_onEvent, const CancelToken &p_cancel) { - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); - const double scale = p_game->GetMaxPayoff() - p_game->GetMinPayoff(); - if (scale != 0.0) { - p_maxregret *= scale; - } + p_maxregret = ScaleRegret(p_game, p_maxregret); std::list> ret; PossibleNashBehaviorSupports possible_supports(p_game); diff --git a/src/solvers/enumpoly/nfgpoly.cc b/src/solvers/enumpoly/nfgpoly.cc index 89301e46a4..bf7f3e6631 100644 --- a/src/solvers/enumpoly/nfgpoly.cc +++ b/src/solvers/enumpoly/nfgpoly.cc @@ -146,15 +146,9 @@ EnumPolyStrategySolve(const Game &p_game, std::optional p_stopAfter, dou EnumPolyEventCallbackType p_onEvent, const CancelToken &p_cancel) { - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); - const double scale = p_game->GetMaxPayoff() - p_game->GetMinPayoff(); - if (scale != 0.0) { - p_maxregret *= scale; - } + p_maxregret = ScaleRegret(p_game, p_maxregret); std::list> ret; PossibleNashStrategySupports possible_supports(p_game); diff --git a/src/solvers/enumpure/enumpure.h b/src/solvers/enumpure/enumpure.h index f6ba6e0ac8..de5af30038 100644 --- a/src/solvers/enumpure/enumpure.h +++ b/src/solvers/enumpure/enumpure.h @@ -57,10 +57,7 @@ inline EnumPureStrategyResult EnumPureStrategySolve( StrategyCallbackType p_onEquilibrium = NullStrategyCallback, const CancelToken &p_cancel = CancelToken()) { - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); EnumPureStrategyResult result; for (const auto &profile : StrategyContingencies(p_game)) { p_cancel.Check(); diff --git a/src/solvers/gnm/gnm.cc b/src/solvers/gnm/gnm.cc index 8e2146ba02..1866dd6c57 100644 --- a/src/solvers/gnm/gnm.cc +++ b/src/solvers/gnm/gnm.cc @@ -88,10 +88,7 @@ GNMStrategyResult GNMStrategySolve(const Game &p_game, double p_lambdaEnd, int p StrategyCallbackType p_onEquilibrium, GNMEventCallbackType p_onEvent, const CancelToken &p_cancel) { - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); const std::shared_ptr A = BuildGame(p_game, true); MixedStrategyProfile pert = p_game->NewMixedStrategyProfile(0.0); for (const auto &player : p_game->GetPlayers()) { @@ -111,10 +108,7 @@ GNMStrategyResult GNMStrategySolve(const MixedStrategyProfile &p_pert, d StrategyCallbackType p_onEquilibrium, GNMEventCallbackType p_onEvent, const CancelToken &p_cancel) { - if (!p_pert.GetGame()->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_pert.GetGame()); const std::shared_ptr A = BuildGame(p_pert.GetGame(), true); return Solve(p_pert.GetGame(), A, ToPerturbation(p_pert), p_lambdaEnd, p_steps, p_localNewtonInterval, p_localNewtonMaxits, p_onEquilibrium, p_onEvent, p_cancel); diff --git a/src/solvers/hp/hp.cc b/src/solvers/hp/hp.cc index dbbc488888..0d520ec389 100644 --- a/src/solvers/hp/hp.cc +++ b/src/solvers/hp/hp.cc @@ -30,6 +30,8 @@ HPStrategyResult HPStrategySolve(const MixedStrategyProfile &p_prior, do StrategyCallbackType p_onEquilibrium, HPEventCallbackType p_onEvent, const CancelToken &p_cancel) { + RequirePerfectRecall(p_prior.GetGame()); + const double maxRegret = ScaleRegret(p_prior.GetGame(), p_maxRegret); HPEquationSystem system(p_prior); Vector x = system.ComputeInitialPoint(); @@ -40,12 +42,12 @@ HPStrategyResult HPStrategySolve(const MixedStrategyProfile &p_prior, do double last_t = 0.0; bool has_crossed = false; - auto termination_condition = [t_target, &last_t, &has_crossed, p_maxRegret, + auto termination_condition = [t_target, &last_t, &has_crossed, p_maxRegret, maxRegret, &system](const Vector &point) { const double t = point[1]; // Path tracer reaches maximum acceptable regret - if (system.ExtractEquilibrium(point).GetMaxRegret() <= p_maxRegret && + if (system.ExtractEquilibrium(point).GetMaxRegret() <= maxRegret && t >= t_target - p_maxRegret) { return true; } @@ -73,9 +75,9 @@ HPStrategyResult HPStrategySolve(const MixedStrategyProfile &p_prior, do return point[1] - t_target; }; - auto polishing_termination_condition = [p_maxRegret, + auto polishing_termination_condition = [maxRegret, &system](const Vector &point) -> bool { - return system.ExtractEquilibrium(point).GetMaxRegret() <= p_maxRegret; + return system.ExtractEquilibrium(point).GetMaxRegret() <= maxRegret; }; const auto tracing_result = tracer.TracePath( @@ -110,7 +112,7 @@ HPStrategyResult HPStrategySolve(const MixedStrategyProfile &p_prior, do return {std::nullopt, false, HPTerminationReason::PolishFailed, stats}; } const MixedStrategyProfile equilibrium = system.ExtractEquilibrium(x); - if (equilibrium.GetMaxRegret() > p_maxRegret) { + if (equilibrium.GetMaxRegret() > maxRegret) { return {std::nullopt, false, HPTerminationReason::RegretTargetNotReached, stats}; } p_onEquilibrium(equilibrium); diff --git a/src/solvers/ipa/ipa.cc b/src/solvers/ipa/ipa.cc index 22c6e20aad..59897fa150 100644 --- a/src/solvers/ipa/ipa.cc +++ b/src/solvers/ipa/ipa.cc @@ -53,6 +53,7 @@ IPAStrategyResult IPAStrategySolve(const Game &p_game, StrategyCallbackType p_onEquilibrium, IPAEventCallbackType p_onEvent, const CancelToken &p_cancel) { + RequirePerfectRecall(p_game); MixedStrategyProfile pert = p_game->NewMixedStrategyProfile(0.0); for (const auto &player : p_game->GetPlayers()) { for (const auto &strategy : player->GetStrategies()) { @@ -69,10 +70,7 @@ IPAStrategyResult IPAStrategySolve(const MixedStrategyProfile &p_pert, StrategyCallbackType p_onEquilibrium, IPAEventCallbackType p_onEvent, const CancelToken &p_cancel) { - if (!p_pert.GetGame()->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_pert.GetGame()); const Game game = p_pert.GetGame(); const std::shared_ptr A = BuildGame(game, false); diff --git a/src/solvers/lcp/efglcp.cc b/src/solvers/lcp/efglcp.cc index bf3b881aee..dba79fc1fe 100644 --- a/src/solvers/lcp/efglcp.cc +++ b/src/solvers/lcp/efglcp.cc @@ -185,10 +185,7 @@ LcpBehaviorResult LcpBehaviorSolve(const Game &p_game, BehaviorCallbackTypeNumPlayers() != 2) { throw UndefinedException("Method only valid for two-player games."); } - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); const ColumnIndexMap columns(p_game); linalg::LemkeTableau tab(ConstructMatrix(columns), ConstructVector(columns)); diff --git a/src/solvers/lcp/nfglcp.cc b/src/solvers/lcp/nfglcp.cc index 37a7e0dbe7..390c75cfb5 100644 --- a/src/solvers/lcp/nfglcp.cc +++ b/src/solvers/lcp/nfglcp.cc @@ -273,10 +273,7 @@ std::list> NashLcpStrategySolver::Solve(const Game &p if (p_game->NumPlayers() != 2) { throw UndefinedException("Method only valid for two-player games."); } - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); Solution solution; const Matrix A1 = Make_A1(p_game); diff --git a/src/solvers/liap/efgliap.cc b/src/solvers/liap/efgliap.cc index 7ef63636f0..212bb6ad1f 100644 --- a/src/solvers/liap/efgliap.cc +++ b/src/solvers/liap/efgliap.cc @@ -38,7 +38,7 @@ class AgentLyapunovFunction : public FunctionOnSimplices { explicit AgentLyapunovFunction(const MixedBehaviorProfile &p_start) : m_game(p_start.GetGame()), m_profile(p_start) { - m_scale = m_game->GetMaxPayoff() - m_game->GetMinPayoff(); + m_scale = static_cast(AgentExpectedPayoffScale(m_game)); m_scale = (m_scale == 0.0) ? 1.0 : 1.0 / m_scale; std::transform( m_game->GetInfosets().begin(), m_game->GetInfosets().end(), std::back_inserter(m_shape), @@ -133,10 +133,7 @@ LiapAgentResult LiapAgentSolve(const MixedBehaviorProfile &p_start, doub LiapEventCallbackType> p_onEvent, const CancelToken &p_cancel) { - if (!p_start.GetGame()->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_start.GetGame()); MixedBehaviorProfile p(p_start); p_onEvent(LiapStartEvent>{p}); diff --git a/src/solvers/liap/nfgliap.cc b/src/solvers/liap/nfgliap.cc index 5b46929421..3635034019 100644 --- a/src/solvers/liap/nfgliap.cc +++ b/src/solvers/liap/nfgliap.cc @@ -37,7 +37,7 @@ class StrategicLyapunovFunction : public FunctionOnSimplices { explicit StrategicLyapunovFunction(const MixedStrategyProfile &p_start) : m_game(p_start.GetGame()), m_profile(p_start) { - m_scale = m_game->GetMaxPayoff() - m_game->GetMinPayoff(); + m_scale = static_cast(ExpectedPayoffScale(m_game)); m_scale = (m_scale == 0.0) ? 1.0 : 1.0 / m_scale; } ~StrategicLyapunovFunction() override = default; @@ -139,10 +139,7 @@ LiapStrategyResult LiapStrategySolve(const MixedStrategyProfile &p_start LiapEventCallbackType> p_onEvent, const CancelToken &p_cancel) { - if (!p_start.GetGame()->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_start.GetGame()); MixedStrategyProfile p(p_start); p_onEvent(LiapStartEvent>{p}); diff --git a/src/solvers/logit/efglogit.cc b/src/solvers/logit/efglogit.cc index 6d779cb973..b34da219d6 100644 --- a/src/solvers/logit/efglogit.cc +++ b/src/solvers/logit/efglogit.cc @@ -67,7 +67,7 @@ Vector ProfileToPoint(const LogitQREMixedBehaviorProfile &p_profile) bool RegretTerminationFunction(const Game &p_game, const Vector &p_point, double p_regret) { - return (p_point.back() < 0.0 || PointToProfile(p_game, p_point).GetAgentMaxRegret() < p_regret); + return (p_point.back() < 0.0 || PointToProfile(p_game, p_point).GetMaxRegret() < p_regret); } // @@ -409,6 +409,7 @@ LogitBehaviorSolve(const LogitQREMixedBehaviorProfile &p_start, double p_regret, LogitEventCallbackType p_onEvent, const CancelToken &p_cancel) { + Nash::RequirePerfectRecall(p_start.GetGame()); if (p_start.size() == 0) { return {{p_start}, {}}; } @@ -416,10 +417,7 @@ LogitBehaviorSolve(const LogitQREMixedBehaviorProfile &p_start, double p_regret, tracer.SetMaxDecel(p_maxAccel); tracer.SetStepsize(p_firstStep); - const double scale = p_start.GetGame()->GetMaxPayoff() - p_start.GetGame()->GetMinPayoff(); - if (scale != 0.0) { - p_regret *= scale; - } + p_regret = Nash::ScaleRegret(p_start.GetGame(), p_regret); const Game game = p_start.GetGame(); Vector x(ProfileToPoint(p_start)); TracingCallbackFunction callback(game, p_onEvent); @@ -444,7 +442,7 @@ LogitBehaviorSolve(const LogitQREMixedBehaviorProfile &p_start, double p_regret, callback.OnPerturbation(p_active, p_point); }); const auto &profiles = callback.GetProfiles(); - if (profiles.back().GetProfile().GetAgentMaxRegret() < p_regret) { + if (profiles.back().GetProfile().GetMaxRegret() < p_regret) { p_onEquilibrium(profiles.back().GetProfile()); } return {profiles, callback.GetBifurcations(), {result.stats}}; diff --git a/src/solvers/logit/logit.h b/src/solvers/logit/logit.h index 6cab430c97..15b21f4cb2 100644 --- a/src/solvers/logit/logit.h +++ b/src/solvers/logit/logit.h @@ -173,8 +173,7 @@ inline LogitStrategyResult LogitStrategySolveEquilibrium( const auto trace = LogitStrategySolve(p_start, p_regret, p_direction, p_firstStep, p_maxAccel, Nash::NullStrategyCallback, p_onEvent, p_cancel); const MixedStrategyProfile &candidate = trace.profiles.back().GetProfile(); - const double scale = p_start.GetGame()->GetMaxPayoff() - p_start.GetGame()->GetMinPayoff(); - const double regret = (scale != 0.0) ? p_regret * scale : p_regret; + const double regret = Nash::ScaleRegret(p_start.GetGame(), p_regret); if (candidate.GetMaxRegret() > regret) { return {std::nullopt, false, LogitTerminationReason::RegretTargetNotReached, trace.bifurcations, trace.stats}; @@ -228,9 +227,8 @@ inline LogitBehaviorResult LogitBehaviorSolveEquilibrium( const auto trace = LogitBehaviorSolve(p_start, p_regret, p_direction, p_firstStep, p_maxAccel, Nash::NullBehaviorCallback, p_onEvent, p_cancel); const MixedBehaviorProfile &candidate = trace.profiles.back().GetProfile(); - const double scale = p_start.GetGame()->GetMaxPayoff() - p_start.GetGame()->GetMinPayoff(); - const double regret = (scale != 0.0) ? p_regret * scale : p_regret; - if (candidate.GetAgentMaxRegret() > regret) { + const double regret = Nash::ScaleRegret(p_start.GetGame(), p_regret); + if (candidate.GetMaxRegret() > regret) { return {std::nullopt, false, LogitTerminationReason::RegretTargetNotReached, trace.bifurcations, trace.stats}; } diff --git a/src/solvers/logit/nfglogit.cc b/src/solvers/logit/nfglogit.cc index 3eda407c4c..4525a399f7 100644 --- a/src/solvers/logit/nfglogit.cc +++ b/src/solvers/logit/nfglogit.cc @@ -367,6 +367,7 @@ LogitStrategySolve(const LogitQREMixedStrategyProfile &p_start, double p_regret, LogitEventCallbackType p_onEvent, const CancelToken &p_cancel) { + Nash::RequirePerfectRecall(p_start.GetGame()); if (p_start.size() == 0) { return {{p_start}, {}}; } @@ -374,10 +375,7 @@ LogitStrategySolve(const LogitQREMixedStrategyProfile &p_start, double p_regret, tracer.SetMaxDecel(p_maxAccel); tracer.SetStepsize(p_firstStep); - if (const double scale = p_start.GetGame()->GetMaxPayoff() - p_start.GetGame()->GetMinPayoff(); - scale != 0.0) { - p_regret *= scale; - } + p_regret = Nash::ScaleRegret(p_start.GetGame(), p_regret); const Game game = p_start.GetGame(); Vector x(ProfileToPoint(p_start)); @@ -414,6 +412,7 @@ LogitLambdaResult LogitStrategySolveLambda( PathTracer::TraceDirection p_direction, double p_firstStep, double p_maxAccel, LogitEventCallbackType p_onEvent) { + Nash::RequirePerfectRecall(p_start.GetGame()); if (p_start.size() == 0) { return {{p_start}, {}}; } diff --git a/src/solvers/lp/lp.cc b/src/solvers/lp/lp.cc index 8ff2d776d3..d4056a2434 100644 --- a/src/solvers/lp/lp.cc +++ b/src/solvers/lp/lp.cc @@ -221,10 +221,7 @@ LpBehaviorResult LpBehaviorSolve(const Game &p_game, BehaviorCallbackType if (!p_game->IsConstSum()) { throw UndefinedException("Method only valid for constant-sum games."); } - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); const TableauIndexMap indexMap(p_game); const Matrix A = ConstructMatrix(indexMap); @@ -256,10 +253,7 @@ LpStrategyResult LpStrategySolve(const Game &p_game, StrategyCallbackType if (!p_game->IsConstSum()) { throw UndefinedException("Method only valid for constant-sum games."); } - if (!p_game->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_game); const int m = p_game->GetPlayer(1)->GetStrategies().size(); const int k = p_game->GetPlayer(2)->GetStrategies().size(); diff --git a/src/solvers/nash.h b/src/solvers/nash.h index be225d41da..cbe2f07a2f 100644 --- a/src/solvers/nash.h +++ b/src/solvers/nash.h @@ -44,6 +44,38 @@ using BehaviorCallbackType = std::function &) /// @brief A fallback callback function for mixed behavior profiles that does nothing template void NullBehaviorCallback(const MixedBehaviorProfile &) {} +/// @brief Throws if the game does not have perfect recall +inline void RequirePerfectRecall(const Game &p_game) +{ + if (!p_game->IsPerfectRecall()) { + throw UndefinedException( + "Computing equilibria of games with imperfect recall is not supported."); + } +} + +/// @brief The width of the range of expected payoffs, used as the unit for regret criteria +inline Rational ExpectedPayoffScale(const Game &p_game) +{ + const auto [minPay, maxPay] = p_game->GetExpectedPayoffRange(); + return maxPay - minPay; +} + +/// @brief The width of the range of expected payoffs of the agent form of the game +inline Rational AgentExpectedPayoffScale(const Game &p_game) +{ + const auto [minPay, maxPay] = p_game->GetAgentExpectedPayoffRange(); + return maxPay - minPay; +} + +/// @brief Converts a maximum regret, expressed as a fraction of the range of expected payoffs, +/// into the game's own payoff units +/// @details If all expected payoffs are equal the regret is returned unchanged. +template T ScaleRegret(const Game &p_game, const T &p_maxRegret) +{ + const Rational scale = ExpectedPayoffScale(p_game); + return (scale == Rational(0)) ? p_maxRegret : p_maxRegret * static_cast(scale); +} + template std::list> ToMixedBehaviorProfile(const std::list> &p_list) diff --git a/src/solvers/simpdiv/simpdiv.cc b/src/solvers/simpdiv/simpdiv.cc index 380bb90826..d9297fc88d 100644 --- a/src/solvers/simpdiv/simpdiv.cc +++ b/src/solvers/simpdiv/simpdiv.cc @@ -504,12 +504,9 @@ inline Integer find_lcd(const Vector &vec) std::list> NashSimpdivStrategySolver::Solve(const MixedStrategyProfile &p_start) const { - if (!p_start.GetGame()->IsPerfectRecall()) { - throw UndefinedException( - "Computing equilibria of games with imperfect recall is not supported."); - } + RequirePerfectRecall(p_start.GetGame()); Rational d(Integer(1), find_lcd(p_start.GetProbVector())); - const Rational scale = p_start.GetGame()->GetMaxPayoff() - p_start.GetGame()->GetMinPayoff(); + const Rational maxRegret = ScaleRegret(p_start.GetGame(), m_maxregret); MixedStrategyProfile y(p_start); m_onEvent(SimpdivStartEvent{y}); @@ -518,7 +515,7 @@ NashSimpdivStrategySolver::Solve(const MixedStrategyProfile &p_start) d /= Rational(m_gridResize); const Rational regret = Simplex(y, d); m_onEvent(SimpdivRefinementEvent{y, d, regret}); - if (regret <= m_maxregret * scale) { + if (regret <= maxRegret) { break; } } @@ -532,6 +529,7 @@ NashSimpdivStrategySolver::Solve(const MixedStrategyProfile &p_start) std::list> NashSimpdivStrategySolver::Solve(const Game &p_game) const { + RequirePerfectRecall(p_game); return Solve(SimpdivDefaultStart(p_game)); } diff --git a/tests/test_games/golden_logit/3_player_nonterm_outcomes.json b/tests/test_games/golden_logit/3_player_nonterm_outcomes.json index f5bc3f2214..7482255514 100644 --- a/tests/test_games/golden_logit/3_player_nonterm_outcomes.json +++ b/tests/test_games/golden_logit/3_player_nonterm_outcomes.json @@ -1,5 +1,5 @@ { - "counts": [{"predictor_attempts": 54, "accepted_steps": 54, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 108, "function_evals": 108, "jacobian_evals": 55, "factorizations": 55}], + "counts": [{"predictor_attempts": 51, "accepted_steps": 51, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 102, "function_evals": 102, "jacobian_evals": 52, "factorizations": 52}], "points": [ [0.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 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b/tests/test_games/golden_logit/strategy_stripped_down_poker.json @@ -1,5 +1,5 @@ { - "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}], + "counts": [{"predictor_attempts": 91, "accepted_steps": 91, "rejected_distance": 0, "rejected_contraction": 0, "rejected_orientation": 0, "corrector_iterations": 169, "function_evals": 169, "jacobian_evals": 92, "factorizations": 92}], "points": [ [0.0, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5], [0.018087976862970135, 0.2533925828167469, 0.2522647687670298, 0.24772261312204105, 0.2466200352943636, 0.5022557549121545, 0.49774424508784587], @@ -22,73 +22,76 @@ [0.8010697122592364, 0.3874151556542515, 0.35039420542170746, 0.13767327039066754, 0.12451736975772197, 0.5830800589587605, 0.41691994097415236], [0.8935793665048571, 0.3999071558420333, 0.3609259970996992, 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0.6656861214550799, 0.6673934297381655, 0.33260657035597946], + [347.4841428993361, 1.0, 0.0, 0.3342242947942512, 0.6657757053533122, 0.6673277429271212, 0.33267225715095106], + [382.2344636066957, 1.0, 0.0, 0.3341429315715547, 0.6658570685500951, 0.6672679609731755, 0.3327320390915471], + [420.4598240622738, 1.0, 0.0, 0.3340690284669076, 0.6659309716334014, 0.6672135587106792, 0.33278644134296076], + [462.50772753555907, 1.0, 0.0, 0.3340018963201774, 0.6659981037625511, 0.6671640566792816, 0.3328359433651618], + [508.76042768838175, 1.0, 0.0, 0.3339409105139823, 0.6660590895542597, 0.6671190173266233, 0.3328809827101915], + [559.6384036079847, 1.0, 0.0, 0.33388550478075957, 0.666114495275542, 0.6670780414931248, 0.3329219585373643] ] } diff --git a/tests/test_nash.py b/tests/test_nash.py index 9cc1f7e2d1..c6205b20d7 100644 --- a/tests/test_nash.py +++ b/tests/test_nash.py @@ -1745,8 +1745,8 @@ def _one_hot_perturbation(rational: bool) -> gbt.MixedStrategyProfile: start_data=dict(data=None, rational=True), expected=[ [ - d(Q(174763, 524288), Q(349525, 524288), 0, 0), - d(Q(699051, 1048576), Q(349525, 1048576)), + d(Q(699051, 2097152), Q(1398101, 2097152), 0, 0), + d(Q(1398101, 2097152), Q(699051, 2097152)), ] ], regret_tol=TOL_LARGE, diff --git a/tests/test_regret_scaling.py b/tests/test_regret_scaling.py new file mode 100644 index 0000000000..1b561b054f --- /dev/null +++ b/tests/test_regret_scaling.py @@ -0,0 +1,64 @@ +"""Tests that `maxregret` is scaled by the same payoff range whether a game is held as a tree +or as an explicit table (issue #1168).""" + +import io + +import pytest + +import pygambit as gbt + +from . import games + + +def _as_table(game: gbt.Game) -> gbt.Game: + return gbt.read_nfg(io.StringIO(game.to_nfg())) + + +def _solve_logit_strategic(game: gbt.Game, maxregret: float): + events = [] + result = gbt.nash.logit_solve( + game, use_strategic=True, maxregret=maxregret, event_callback=events.append + ) + return result, sum(isinstance(e, gbt.LogitPathEvent) for e in events) + + +@pytest.mark.parametrize( + "factory", + [games.create_stripped_down_poker_efg, games.create_kuhn_poker_efg], + ids=["stripped_down_poker", "kuhn_poker"], +) +@pytest.mark.parametrize("maxregret", [1.0e-1, 1.0e-2, 1.0e-4]) +def test_logit_strategic_termination_same_for_tree_and_table(factory, maxregret): + tree = factory() + table = _as_table(tree) + # The ranges of single plays differ; only the expected payoff range is common to both. + assert (tree.min_payoff, tree.max_payoff) != (table.min_payoff, table.max_payoff) + + tree_result, tree_points = _solve_logit_strategic(tree, maxregret) + table_result, table_points = _solve_logit_strategic(table, maxregret) + + assert tree_result.success and table_result.success + assert tree_points == table_points + for player in table.players: + for strategy in table.get_strategies(player): + assert tree_result.equilibrium[player][strategy] == pytest.approx( + table_result.equilibrium[player][strategy], abs=1.0e-9 + ) + + +@pytest.mark.parametrize("maxregret", [1.0e-1, 1.0e-2, 1.0e-4]) +def test_hp_termination_same_for_tree_and_table(maxregret): + tree = games.create_stripped_down_poker_efg() + table = _as_table(tree) + + def solve(game): + events = [] + result = gbt.nash.hp_solve( + game.mixed_strategy_profile(), maxregret=maxregret, event_callback=events.append + ) + return result, len(events) + + tree_result, tree_points = solve(tree) + table_result, table_points = solve(table) + assert tree_result.success and table_result.success + assert tree_points == table_points diff --git a/tests/test_tree_strategy_values.py b/tests/test_tree_strategy_values.py new file mode 100644 index 0000000000..94b74d17e6 --- /dev/null +++ b/tests/test_tree_strategy_values.py @@ -0,0 +1,95 @@ +"""Tests of the strategy payoffs of mixed strategy profiles on game trees. + +The regret and Liapunov value of a profile are computed from all of the players' strategy payoffs +at once. On trees with perfect recall these are computed from sequences; they are compared with +the payoffs of the strategies computed one at a time. +""" + +import random +import time + +import pytest + +import pygambit as gbt + +from . import games + + +def _interior_profile(game: gbt.Game, seed: int, *, rational: bool = False): + rng = random.Random(seed) + data = [] + for player in game.players: + weights = [rng.randint(1, 9) for _ in game.get_strategies(player)] + total = sum(weights) + data.append([gbt.Rational(w, total) if rational else w / total for w in weights]) + return game.mixed_strategy_profile(data=data, rational=rational) + + +def _reference(profile): + """Max regret and Liapunov value from the payoffs of the strategies one at a time.""" + payoffs = profile.payoffs + values = profile.strategy_values + regrets = {p: max(v for _, v in values[p]) - payoffs[p] for p in profile.game.players} + liap = sum(max(v - payoffs[p], 0) ** 2 for p in profile.game.players for _, v in values[p]) + return max(regrets.values()), liap, regrets + + +def _n_types_game(n: int) -> gbt.Game: + game = gbt.ExtensiveGame(players=["1", "2"]) + game.append_event(gbt.H.path(), {f"t{i}": gbt.Rational(1, n) for i in range(n)}) + for i in range(n): + game.append_move(gbt.H.path(f"t{i}"), "1", ["a", "b"]) + game.make_outcome(gbt.H.path(f"t{i}", "a"), {"1": 1, "2": 0}, f"w{i}") + return game + + +PERFECT_RECALL = [ + pytest.param(games.create_stripped_down_poker_efg(), id="poker"), + pytest.param( + games.read_from_file("chance_in_middle_with_nonterm_outcomes.efg"), + id="chance-in-middle-nonterminal-outcomes", + ), + pytest.param(games.read_from_file("basic_extensive_game.efg"), id="basic"), +] + + +@pytest.mark.parametrize("game", PERFECT_RECALL) +def test_double_matches_per_strategy_path(game: gbt.Game): + profile = _interior_profile(game, seed=1) + max_regret, liap, _ = _reference(profile) + assert profile.max_regret() == pytest.approx(max_regret, abs=1e-12) + assert profile.liap_value() == pytest.approx(liap, abs=1e-12) + + +@pytest.mark.parametrize("game", PERFECT_RECALL) +def test_rational_matches_per_strategy_path_exactly(game: gbt.Game): + profile = _interior_profile(game, seed=2, rational=True) + max_regret, liap, _ = _reference(profile) + assert profile.max_regret() == max_regret + assert profile.liap_value() == liap + + +@pytest.mark.parametrize("game", PERFECT_RECALL) +def test_pure_profile_matches_per_strategy_path(game: gbt.Game): + profile = game.mixed_strategy_profile(rational=True) + max_regret, liap, _ = _reference(profile) + assert profile.max_regret() == max_regret + assert profile.liap_value() == liap + + +def test_imperfect_recall_falls_back_via_conversion_constructor(): + game = games.read_from_file("gilboa_two_am_agents.efg") + assert not game.is_perfect_recall + behavior = game.mixed_behavior_profile(rational=True) + profile = behavior.as_strategy() + max_regret, liap, _ = _reference(profile) + assert profile.max_regret() == max_regret + assert profile.liap_value() == liap + + +def test_n_types_regret_is_fast(): + game = _n_types_game(12) + profile = game.mixed_strategy_profile() + start = time.perf_counter() + profile.max_regret() + assert time.perf_counter() - start < 1.0