Bernhard catalog 7 games

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
 

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
 
 

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#vS22>`_.
+It is essentially a type of poker game.
+Its description as a competition between software firms is due to
+`TvS02 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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}

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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 <https://gambitproject.readthedocs.io/en/latest/biblio.html#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 }

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.