From be6ad92f9444a7dc6fdc470d3ab7d9e836c55be1 Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Fri, 22 May 2026 23:21:50 +0300 Subject: [PATCH 1/9] add {vSF08,TvS02,vS22} to biblio.rst and other missing bib details --- doc/biblio.rst | 31 +++++++++++++++++++++---------- 1 file changed, 21 insertions(+), 10 deletions(-) diff --git a/doc/biblio.rst b/doc/biblio.rst index 28c4e7ce6..7a20e9ebb 100644 --- a/doc/biblio.rst +++ b/doc/biblio.rst @@ -9,8 +9,8 @@ Bibliography -Articles on computation of Nash equilibria ------------------------------------------- +Articles on computation of equilibria +------------------------------------- .. [BlaTur23] Bland, J. R. and Turocy, T. L. 2023, 'Quantal response equilibrium as a structural model for estimation: the @@ -53,12 +53,12 @@ Articles on computation of Nash equilibria pp. 87-142. .. [Nau2004] Nau, Robert, Gomez Canovas, Sabrina, and Hansen, Pierre (2004). - On the geometry of Nash equilibria and correlated equilibria. - International Journal of Game Theory 32(4): 443-453 + 'On the geometry of Nash equilibria and correlated equilibria', + *International Journal of Game Theory*, vol. 32, pp. 443-453. .. [PNS04] Porter, R., Nudelman, E. and Shoham, Y. 2004, 'Simple search methods for finding a Nash equilibrium', - *Games and Economic Behavior*, pp. 664-669. + *Games and Economic Behavior*, vol. 63, pp. 664-662. .. [Ros71] Rosenmuller, J. 1971, 'On a generalization of the Lemke-Howson algorithm to noncooperative @@ -75,19 +75,23 @@ Articles on computation of Nash equilibria .. [Tur10] Turocy, T. L. 2010, 'Using quantal response to compute Nash and sequential equilibria', - *Economic Theory*, vol. 42, no. 1, pp. 255-269. + *Economic Theory*, vol. 42, pp. 255-269. .. [VTH87] van der Laan, G., Talman, A. J. J. and van Der Heyden, L. 1987, 'Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general - labelling', *Mathematics of Operations Research*, pp. 377-397. + labelling', *Mathematics of Operations Research*, vol. 12, pp. 377-397. + +.. [vSF08] von Stengel, B. and Forges, F., 2008, + 'Extensive-form correlated equilibrium: Definition and computational complexity', + *Mathematics of Operations Research*, vol. 33, pp. 1002–1022. .. [Wil71] Wilson, R. 1971, 'Computing equilibria of n-person games', *SIAM Applied Math*, vol. 21, pp. 80-87. .. [Yam93] Yamamoto, Y. 1993, 'A path-following procedure to find a proper equilibrium of finite - games', *International Journal of Game Theory*. + games', *International Journal of Game Theory*, vol. 22, pp. 249–259. @@ -158,11 +162,18 @@ General game theory articles and texts -Textbooks and general reference -------------------------------- +Textbooks and general references +-------------------------------- .. [Mye91] Myerson, R. 1991, *Game Theory: Analysis of Conflict*, Harvard University Press. +.. [TvS02] Turocy, T.L. and von Stengel, B., 2002, + 'Game theory', in: *Encyclopedia of Information Systems*, vol. 2, pp. 403–420, + Elsevier Science. + +.. [vS22] von Stengel, B., 2022, *Game Theory Basics*, + Cambridge University Press. + .. [Wat13] Watson, J. 2013, *Strategy: An Introduction to Game Theory*, 3rd edn, W. W. Norton & Company. From 313618e4fe9df3e4579d7785c38b191c1727d63e Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Sat, 23 May 2026 10:38:21 +0300 Subject: [PATCH 2/9] fig 6 from vonstengelforges2008 (figs 1 and 9 to come) --- catalog/vonstengelforges2008/fig6.efg | 31 +++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 catalog/vonstengelforges2008/fig6.efg diff --git a/catalog/vonstengelforges2008/fig6.efg b/catalog/vonstengelforges2008/fig6.efg new file mode 100644 index 000000000..fb262b4f6 --- /dev/null +++ b/catalog/vonstengelforges2008/fig6.efg @@ -0,0 +1,31 @@ +EFG 2 R "Figure 6 from von Stengel and Forges (2008)" { "1" "2" } +" +Figure 6 from `vSF08 `_. +This game has perfect recall, but with a circular precedence structure among the information sets +of the two players. +" + + +p "" 2 1 "" { "a" "b" } 0 +p "" 1 1 "" { "L" "R" } 0 +p "" 1 2 "" { "S" "T" } 0 +t "" 1 "" { 0 0 } +p "" 2 2 "" { "c" "d" } 0 +t "" 2 "" { 0 0 } +t "" 3 "" { 0 0 } +p "" 2 2 0 +t "" 4 "" { 0 0 } +p "" 1 3 "" { "U" "V" } 0 +t "" 5 "" { 0 0 } +t "" 6 "" { 0 0 } +p "" 1 1 0 +p "" 2 3 "" { "e" "f" } 0 +p "" 1 2 0 +t "" 7 "" { 0 0 } +t "" 8 "" { 0 0 } +t "" 9 "" { 0 0 } +p "" 1 3 0 +t "" 10 "" { 0 0 } +p "" 2 3 0 +t "" 11 "" { 0 0 } +t "" 12 "" { 0 0 } From 7eef2d32f7dc95157c7262c6fff56e3dc01d8c93 Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Sat, 23 May 2026 14:29:10 +0300 Subject: [PATCH 3/9] note that vonstengelforges08/fig6.efg has no chance moves --- Makefile.am | 1 + catalog/vonstengelforges2008/fig6.efg | 4 ++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/Makefile.am b/Makefile.am index f07dd5034..a5d755f17 100644 --- a/Makefile.am +++ b/Makefile.am @@ -221,6 +221,7 @@ EXTRA_DIST = \ catalog/selten1975/fig1.efg \ catalog/selten1975/fig2.efg \ catalog/selten1975/fig3.efg \ + catalog/vonstengelforges2008/fig6.efg \ catalog/watson2013/exercise29_6.efg \ catalog/watson2013/fig29_1.efg diff --git a/catalog/vonstengelforges2008/fig6.efg b/catalog/vonstengelforges2008/fig6.efg index fb262b4f6..db627982c 100644 --- a/catalog/vonstengelforges2008/fig6.efg +++ b/catalog/vonstengelforges2008/fig6.efg @@ -1,8 +1,8 @@ EFG 2 R "Figure 6 from von Stengel and Forges (2008)" { "1" "2" } " Figure 6 from `vSF08 `_. -This game has perfect recall, but with a circular precedence structure among the information sets -of the two players. +This game has perfect recall and not chance moves, yet it has a circular precedence structure among +the information sets of the two players. " From 09f518c36b4b258f5d66c271d92987065cb14e33 Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Sat, 23 May 2026 22:30:07 +0300 Subject: [PATCH 4/9] added catalog/vonstengel2022/ --- Makefile.am | 4 ++++ catalog/vonstengel2022/fig10.1.efg | 19 +++++++++++++++++++ catalog/vonstengel2022/fig10.12.efg | 21 +++++++++++++++++++++ catalog/vonstengel2022/fig10.5.efg | 22 ++++++++++++++++++++++ catalog/vonstengel2022/fig10.7.efg | 26 ++++++++++++++++++++++++++ catalog/vonstengelforges2008/fig6.efg | 4 ++-- 6 files changed, 94 insertions(+), 2 deletions(-) create mode 100644 catalog/vonstengel2022/fig10.1.efg create mode 100644 catalog/vonstengel2022/fig10.12.efg create mode 100644 catalog/vonstengel2022/fig10.5.efg create mode 100644 catalog/vonstengel2022/fig10.7.efg diff --git a/Makefile.am b/Makefile.am index a5d755f17..67fd6317e 100644 --- a/Makefile.am +++ b/Makefile.am @@ -221,6 +221,10 @@ EXTRA_DIST = \ catalog/selten1975/fig1.efg \ catalog/selten1975/fig2.efg \ catalog/selten1975/fig3.efg \ + catalog/vonstengel2022/fig10.1.efg \ + catalog/vonstengel2022/fig10.12.efg \ + catalog/vonstengel2022/fig10.5.efg \ + catalog/vonstengel2022/fig10.7.efg \ catalog/vonstengelforges2008/fig6.efg \ catalog/watson2013/exercise29_6.efg \ catalog/watson2013/fig29_1.efg diff --git a/catalog/vonstengel2022/fig10.1.efg b/catalog/vonstengel2022/fig10.1.efg new file mode 100644 index 000000000..f94d07eab --- /dev/null +++ b/catalog/vonstengel2022/fig10.1.efg @@ -0,0 +1,19 @@ +EFG 2 R "Figure 10.1 from von Stengel (2022)" { "I" "II" } +" +Figure 10.1 from `vS22 `_. +It is essentially a type of poker game. +Its description as a competition between software firms is due to +`TvS02 `_. +" + +c "" 1 "" { "1/2" 1/2 "1/2" 1/2 } 0 +p "" 1 1 "" { "T" "B" } 0 +t "" 1 "" { 0 16 } +p "" 2 1 "" { "a" "b" } 0 +t "" 2 "" { 12 4 } +t "" 3 "" { -4 20 } +p "" 1 2 "" { "C" "D" } 0 +t "" 4 "" { 0 16 } +p "" 2 1 0 +t "" 5 "" { 12 4 } +t "" 6 "" { 20 -4} diff --git a/catalog/vonstengel2022/fig10.12.efg b/catalog/vonstengel2022/fig10.12.efg new file mode 100644 index 000000000..44bcd679b --- /dev/null +++ b/catalog/vonstengel2022/fig10.12.efg @@ -0,0 +1,21 @@ +EFG 2 R "Figure 10.12 from von Stengel (2022)" { "I" "II" } +" +Figure 10.12 from `vS22 `_. +It refers to a non-standard version of the Monty Hall problem where the television show host Monty +Hall has the option of opening another door without a prize to the contestant (player I), rather +than opening such a door all the time. Its purpose is to demonstrate a whole convex set of optimal +strategies for player II. +" + + +c "" 1 "" { "1/3" 1/3 "2/3" 2/3 } 0 +p "" 2 1 "" { "C" "O" } 0 +t "" 1 "" { 1 -1 } +p "" 1 1 "" { "K" "S" } 0 +t "" 2 "" { 1 -1 } +t "" 3 "" { 0 0 } +p "" 2 2 "" { "c" "o" } 0 +t "" 4 "" { 0 0 } +p "" 1 1 0 +t "" 5 "" { 0 0 } +t "" 6 "" { 1 -1 } diff --git a/catalog/vonstengel2022/fig10.5.efg b/catalog/vonstengel2022/fig10.5.efg new file mode 100644 index 000000000..637a9db22 --- /dev/null +++ b/catalog/vonstengel2022/fig10.5.efg @@ -0,0 +1,22 @@ +EFG 2 R "Figure 10.5 from von Stengel (2022)" { "I" "II" } +" +Figure 10.5 from `vS22 `_. +Player II has four reduced strategies in this game, compared to eight unreduced strategies. +" + + +p "" 2 1 "" { "l" "r" } 0 +p "" 1 1 "" { "T" "B" } 0 +p "" 2 2 "" { "a" "b" } 0 +t "" 1 "" { 1 5 } +t "" 2 "" { 3 4 } +p "" 2 2 0 +t "" 3 "" { 0 0 } +t "" 4 "" { 0 2 } +p "" 1 1 0 +p "" 2 3 "" { "c" "d" } 0 +t "" 5 "" { 0 3 } +t "" 6 "" { 1 0 } +p "" 2 3 0 +t "" 7 "" { 2 3 } +t "" 8 "" { 0 4 } diff --git a/catalog/vonstengel2022/fig10.7.efg b/catalog/vonstengel2022/fig10.7.efg new file mode 100644 index 000000000..d4f9bc1b6 --- /dev/null +++ b/catalog/vonstengel2022/fig10.7.efg @@ -0,0 +1,26 @@ +EFG 2 R "Figure 10.7 from von Stengel (2022)" { "I" "II" } +" +Figure 10.7 from `vS22 `_. +It is a game with imperfect recall, but it has the same strategic form as the game in Figure 10.5 +from the same book. +One equilibrium strategy of player II as computed from the strategic form is not realization +equivalent to any behavior strategy, namely the mixed strategy (0, 2/5, 3/5, 0) +for (la, lb, ra, rb). +" + + +p "" 2 1 "" { "l" "r" } 0 +p "" 1 1 "" { "T" "B" } 0 +p "" 2 2 "" { "a" "b" } 0 +t "" 1 "" { 1 5 } +t "" 2 "" { 3 4 } +p "" 2 2 0 +t "" 3 "" { 0 0 } +t "" 4 "" { 0 2 } +p "" 1 1 0 +p "" 2 2 0 +t "" 5 "" { 0 3 } +t "" 6 "" { 1 0 } +p "" 2 2 0 +t "" 7 "" { 2 3 } +t "" 8 "" { 0 4 } diff --git a/catalog/vonstengelforges2008/fig6.efg b/catalog/vonstengelforges2008/fig6.efg index db627982c..8a798de32 100644 --- a/catalog/vonstengelforges2008/fig6.efg +++ b/catalog/vonstengelforges2008/fig6.efg @@ -1,8 +1,8 @@ EFG 2 R "Figure 6 from von Stengel and Forges (2008)" { "1" "2" } " Figure 6 from `vSF08 `_. -This game has perfect recall and not chance moves, yet it has a circular precedence structure among -the information sets of the two players. +This game has perfect recall and no chance moves, yet it has a circular precedence structure among +the information sets of the two players. The payoffs are not important. " From e996627c38629950349bbf337b0d35ef74b48c00 Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Sun, 24 May 2026 08:42:51 +0300 Subject: [PATCH 5/9] draw_tree params for vonstengel2022/fig10.1 --- build_support/catalog/update.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/build_support/catalog/update.py b/build_support/catalog/update.py index 0d44b3cc6..0f26d8572 100644 --- a/build_support/catalog/update.py +++ b/build_support/catalog/update.py @@ -26,6 +26,9 @@ def catalog_draw_tree_settings(slug: str) -> dict: settings["action_label_position"] = 0.4 elif "selten1975" in slug: settings["shared_terminal_depth"] = False + elif slug == "vonstengel2022/fig10.1": + settings["sublevel_scaling"] = 0.75 + settings["shared_terminal_depth"] = False return settings From b56d42ddfc9cbaedd9ff0dff8002906dbb366f2e Mon Sep 17 00:00:00 2001 From: Rahul Savani Date: Thu, 28 May 2026 04:19:17 +0100 Subject: [PATCH 6/9] fig1 and fig9 from vonstengelforges2008 --- Makefile.am | 2 ++ build_support/catalog/update.py | 4 ++++ catalog/vonstengelforges2008/fig1.efg | 20 ++++++++++++++++++ catalog/vonstengelforges2008/fig9.efg | 29 +++++++++++++++++++++++++++ 4 files changed, 55 insertions(+) create mode 100644 catalog/vonstengelforges2008/fig1.efg create mode 100644 catalog/vonstengelforges2008/fig9.efg diff --git a/Makefile.am b/Makefile.am index 67fd6317e..3fd8f4f5f 100644 --- a/Makefile.am +++ b/Makefile.am @@ -225,7 +225,9 @@ EXTRA_DIST = \ catalog/vonstengel2022/fig10.12.efg \ catalog/vonstengel2022/fig10.5.efg \ catalog/vonstengel2022/fig10.7.efg \ + catalog/vonstengelforges2008/fig1.efg \ catalog/vonstengelforges2008/fig6.efg \ + catalog/vonstengelforges2008/fig9.efg \ catalog/watson2013/exercise29_6.efg \ catalog/watson2013/fig29_1.efg diff --git a/build_support/catalog/update.py b/build_support/catalog/update.py index 0f26d8572..0b6c03074 100644 --- a/build_support/catalog/update.py +++ b/build_support/catalog/update.py @@ -29,6 +29,10 @@ def catalog_draw_tree_settings(slug: str) -> dict: elif slug == "vonstengel2022/fig10.1": settings["sublevel_scaling"] = 0.75 settings["shared_terminal_depth"] = False + elif slug == "vonstengelforges2008/fig1": + settings["sublevel_scaling"] = 1 + elif slug == "vonstengelforges2008/fig9": + settings["sublevel_scaling"] = 0.5 return settings diff --git a/catalog/vonstengelforges2008/fig1.efg b/catalog/vonstengelforges2008/fig1.efg new file mode 100644 index 000000000..c1add3ecf --- /dev/null +++ b/catalog/vonstengelforges2008/fig1.efg @@ -0,0 +1,20 @@ +EFG 2 R "Figure 1 from von Stengel and Forges (2008)" { "1" "2" } +" +Figure 1 from `vSF08 `_. +" + +c "" 1 "" { "1/2" 1/2 "1/2" 1/2 } 0 +p "" 1 1 "" { "X_G" "Y_G" } 0 +p "" 2 1 "" { "l_X" "r_X" } 0 +t "" 1 "" { 4 10 } +t "" 2 "" { 0 6 } +p "" 2 2 "" { "l_Y" "r_Y" } 0 +t "" 3 "" { 4 10 } +t "" 4 "" { 0 6 } +p "" 1 2 "" { "X_B" "X_G" } 0 +p "" 2 1 0 +t "" 5 "" { 6 0 } +t "" 6 "" { 0 6 } +p "" 2 2 0 +t "" 7 "" { 6 0 } +t "" 8 "" { 0 6 } diff --git a/catalog/vonstengelforges2008/fig9.efg b/catalog/vonstengelforges2008/fig9.efg new file mode 100644 index 000000000..7187b347a --- /dev/null +++ b/catalog/vonstengelforges2008/fig9.efg @@ -0,0 +1,29 @@ +EFG 2 R "Figure 9 from von Stengel and Forges (2008)" { "1" "2" } +" +Figure 9 from `vSF08 `_. +It encodes the SAT formula :math:`x\wedge (\neg x \vee y) \wedge (\neg x \vee \neg y)` +(writing $-x$ for :math:`\neg x`). +The formula is satisfiable (which here it is not) if and only +if the players can ensure a payoff of~1, with a strategy of +player~1 representing the corresponding truth assignment. +" + +c "" 1 "" { "1/3" 1/3 "1/3" 1/3 "1/3" 1/3 } 0 +p "" 2 1 "" { "x" } 0 +p "" 1 1 "" { "x" "-x" } 0 +t "" 1 "" { 1 1 } +t "" 2 "" { 0 0 } +p "" 2 2 "" { "-x" "y" } 0 +p "" 1 1 0 +t "" 3 "" { 0 0 } +t "" 4 "" { 1 1 } +p "" 1 2 "" { "y" "-y" } 0 +t "" 5 "" { 1 1 } +t "" 6 "" { 0 0 } +p "" 2 3 "" { "-x" "-y" } 0 +p "" 1 1 0 +t "" 7 "" { 0 0 } +t "" 8 "" { 1 1 } +p "" 1 2 0 +t "" 9 "" { 0 0 } +t "" 10 "" { 1 1 } From 06f4d33bf69ab20d10f229ed049f44c42acf5f01 Mon Sep 17 00:00:00 2001 From: Rahul Savani Date: Thu, 28 May 2026 05:32:09 +0100 Subject: [PATCH 7/9] remove tildes in fig9 comment --- catalog/vonstengelforges2008/fig9.efg | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/catalog/vonstengelforges2008/fig9.efg b/catalog/vonstengelforges2008/fig9.efg index 7187b347a..db76a8f6a 100644 --- a/catalog/vonstengelforges2008/fig9.efg +++ b/catalog/vonstengelforges2008/fig9.efg @@ -4,8 +4,8 @@ Figure 9 from `vSF08 Date: Thu, 28 May 2026 07:14:37 +0100 Subject: [PATCH 8/9] extend comment in fig 1 --- catalog/vonstengelforges2008/fig1.efg | 1 + 1 file changed, 1 insertion(+) diff --git a/catalog/vonstengelforges2008/fig1.efg b/catalog/vonstengelforges2008/fig1.efg index c1add3ecf..5c74de79d 100644 --- a/catalog/vonstengelforges2008/fig1.efg +++ b/catalog/vonstengelforges2008/fig1.efg @@ -1,6 +1,7 @@ EFG 2 R "Figure 1 from von Stengel and Forges (2008)" { "1" "2" } " Figure 1 from `vSF08 `_. +It is a kind of a kind of signaling game. " c "" 1 "" { "1/2" 1/2 "1/2" 1/2 } 0 From b738b8ddcdc788b9aa1ac961528890104f7b62b4 Mon Sep 17 00:00:00 2001 From: rahulsavani Date: Thu, 28 May 2026 08:14:36 +0100 Subject: [PATCH 9/9] extend comment for fig 9 --- catalog/vonstengelforges2008/fig9.efg | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/catalog/vonstengelforges2008/fig9.efg b/catalog/vonstengelforges2008/fig9.efg index db76a8f6a..6850a0865 100644 --- a/catalog/vonstengelforges2008/fig9.efg +++ b/catalog/vonstengelforges2008/fig9.efg @@ -4,8 +4,9 @@ Figure 9 from `vSF08