From 1c97d4705ae4c582875aa011dec604817c37a128 Mon Sep 17 00:00:00 2001 From: Rahul Savani Date: Tue, 18 Aug 2026 09:56:18 +0100 Subject: [PATCH 1/3] catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg --- build_support/catalog/catalog.am | 1 + .../6x6_game_with_75_eq_small_payoffs.nfg | 49 +++++++++++++++++++ 2 files changed, 50 insertions(+) create mode 100644 catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg diff --git a/build_support/catalog/catalog.am b/build_support/catalog/catalog.am index 9c461ec62e..cde07fd95a 100644 --- a/build_support/catalog/catalog.am +++ b/build_support/catalog/catalog.am @@ -30,6 +30,7 @@ CATALOG_FILES = \ catalog/conf/itcs/jakobsen2016/fig1c.efg \ catalog/conf/itcs/jakobsen2016/fig3.efg \ catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq.nfg \ + catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg \ catalog/journals/geb/bagwell1995.efg \ catalog/journals/geb/gilboa1997/fig1.efg \ catalog/journals/geb/gilboa1997/fig2.efg \ diff --git a/catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg b/catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg new file mode 100644 index 0000000000..ba71107aaa --- /dev/null +++ b/catalog/journals/dcg/vonstengel1999/6x6_game_with_75_eq_small_payoffs.nfg @@ -0,0 +1,49 @@ +NFG 1 R "von Stengel's 6x6 bimatrix game with 75 equilibria (small payoffs)" { "1" "2" } + +{ { "1" "2" "3" "4" "5" "6" } +{ "1" "2" "3" "4" "5" "6" } +} +"Taken from :cite:p:`SvS06`, this version has much smaller payoffs than the original version from +:cite:p:`vS97` and referenced in :cite:p:`vS99`, which is also in this folder of the catalog. +It is a 6x6 bimatrix game with 75 equilibria, +which is more than the previously conjectured bound of :math:`2^6 - 1 = 63`." + +{ +{ "" -81, 72 } +{ "" -180, -180 } +{ "" 20, 297 } +{ "" -30, -333 } +{ "" 270, 270 } +{ "" 90, -153 } +{ "" 36, 36 } +{ "" 72, -81 } +{ "" -3, 126 } +{ "" 17, -126 } +{ "" -153, 90 } +{ "" -36, -36 } +{ "" -126, 17 } +{ "" -333, -30 } +{ "" 42, 42 } +{ "" -33, -33 } +{ "" 297, 20 } +{ "" 126, -3 } +{ "" 126, -3 } +{ "" 297, 20 } +{ "" -33, -33 } +{ "" 42, 42 } +{ "" -333, -30 } +{ "" -126, 17 } +{ "" -36, -36 } +{ "" -153, 90 } +{ "" 17, -126 } +{ "" -3, 126 } +{ "" 72, -81 } +{ "" 36, 36 } +{ "" 90, -153 } +{ "" 270, 270 } +{ "" -30, -333 } +{ "" 20, 297 } +{ "" -180, -180 } +{ "" -81, 72 } +} +1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 From 0938664dddc2a7f7ff6354ed240380bbcb5cf41b Mon Sep 17 00:00:00 2001 From: Rahul Savani Date: Tue, 18 Aug 2026 10:48:22 +0100 Subject: [PATCH 2/3] add SvS06 to references.bib --- doc/references.bib | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/doc/references.bib b/doc/references.bib index 9c5e45b883..74d8c6f6a7 100644 --- a/doc/references.bib +++ b/doc/references.bib @@ -443,3 +443,14 @@ @techreport{vS97 note = {Technical Report 264, Departement Informatik}, category = {articles_equilibria} } + +@article{SvS06, + author = {Rahul Savani and Bernhard von Stengel}, + title = {Hard-to-Solve Bimatrix Games}, + journal = {Econometrica}, + volume = {74}, + number = {2}, + pages = {397--429}, + year = {2006}, + category = {articles_equilibria} +} From c6cbf222525397643f2cfbea848393328ac6f7aa Mon Sep 17 00:00:00 2001 From: Rahul Savani Date: Tue, 18 Aug 2026 11:24:38 +0100 Subject: [PATCH 3/3] consistent first names/initials in references.bib --- doc/references.bib | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/doc/references.bib b/doc/references.bib index 74d8c6f6a7..1998c5ef4e 100644 --- a/doc/references.bib +++ b/doc/references.bib @@ -110,7 +110,7 @@ @incollection{McKMcL96 } @article{Nau2004, - author = {Nau, Robert and Gomez Canovas, Sabrina and Hansen, Pierre}, + author = {Nau, R. and Gomez Canovas, S. and Hansen, P.}, title = {On the geometry of {N}ash equilibria and correlated equilibria}, journal = {International Journal of Game Theory}, volume = {32}, @@ -383,7 +383,7 @@ @book{vS22 } @book{Wat13, - author = {Watson, Joel}, + author = {Watson, J.}, title = {Strategy: An Introduction to Game Theory}, edition = {3rd}, publisher = {W. W. Norton \& Company}, @@ -418,7 +418,7 @@ @article{Wichardt2008 @book{ShoLeyB08, title={Multiagent systems: Algorithmic, game-theoretic, and logical foundations}, - author={Shoham, Yoav and Leyton-Brown, Kevin}, + author={Shoham, Y. and Leyton-Brown, K.}, year={2008}, publisher={Cambridge University Press}, category = {textbooks} @@ -426,7 +426,7 @@ @book{ShoLeyB08 @article{vS99, title = {New Maximal Numbers of Equilibria in Bimatrix Games}, - author = {Bernhard von Stengel}, + author = {von Stengel, B.}, journal = {Discrete Comput. Geom.}, volume = {21}, number = {4}, @@ -436,7 +436,7 @@ @article{vS99 } @techreport{vS97, - author = {Bernhard von Stengel}, + author = {von Stengel, B.}, title = {New lower bounds for the number of equilibria in bimatrix games}, institution = {ETH Z\"urich}, year = {1997}, @@ -445,7 +445,7 @@ @techreport{vS97 } @article{SvS06, - author = {Rahul Savani and Bernhard von Stengel}, + author = {Savani, R. and von Stengel, B.}, title = {Hard-to-Solve Bimatrix Games}, journal = {Econometrica}, volume = {74},