diff --git a/Makefile.am b/Makefile.am index f07dd5034..3fd8f4f5f 100644 --- a/Makefile.am +++ b/Makefile.am @@ -221,6 +221,13 @@ 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/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 0d44b3cc6..0b6c03074 100644 --- a/build_support/catalog/update.py +++ b/build_support/catalog/update.py @@ -26,6 +26,13 @@ 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 + elif slug == "vonstengelforges2008/fig1": + settings["sublevel_scaling"] = 1 + elif slug == "vonstengelforges2008/fig9": + settings["sublevel_scaling"] = 0.5 return settings 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/fig1.efg b/catalog/vonstengelforges2008/fig1.efg new file mode 100644 index 000000000..5c74de79d --- /dev/null +++ b/catalog/vonstengelforges2008/fig1.efg @@ -0,0 +1,21 @@ +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 +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/fig6.efg b/catalog/vonstengelforges2008/fig6.efg new file mode 100644 index 000000000..8a798de32 --- /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 and no chance moves, yet it has a circular precedence structure among +the information sets of the two players. The payoffs are not important. +" + + +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 } diff --git a/catalog/vonstengelforges2008/fig9.efg b/catalog/vonstengelforges2008/fig9.efg new file mode 100644 index 000000000..6850a0865 --- /dev/null +++ b/catalog/vonstengelforges2008/fig9.efg @@ -0,0 +1,30 @@ +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 in any Nash Equilibrium, Correlated Equilibrium, +or Extensive-Form Correlated Equilibrium, +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 } 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.