Enumeration of Nash equilibria for two-player games

Audet C., Belhaï za S., Hansen P.: Enumeration of all extreme equilibria in game theory: bimatrix and polymatrix games. J Optim Theory Appl 129, 349–372 (2006)

Audet, C., Belhaï za, S., Hansen, P.: A new sequence form approach for the enumeration of all extreme Nash equilibria for extensive form games. Int Game Theory Rev, to appear (2009)

Audet C., Hansen P., Jaumard B., Savard G.: Enumeration of all extreme equilibria of bimatrix games. SIAM J Sci Comput 23, 323–338 (2001)

Avis, D. lrs: a revised implementation of the reverse search vertex enumeration algorithm. In: Kalai, G., Ziegler, G. (eds.): Polytopes—Combinatorics and Computation, DMV Seminar Band 29, pp. 177–198. Basel: Birkhäuser (2000)

Avis, D.: User’s Guide for lrs. http://cgm.cs.mcgill.ca/~avis (2006)

Avis D., Fukuda K.: A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete Comput Geom 8, 295–313 (1992)

Avis D., Bremner D., Seidel R.: How good are convex hull algorithms?. Comput Geom 7, 265–301 (1997)

Azulay D.-O., Pique J.-F.: A revised simplex method with integer Q-matrices. ACM Trans Math Softw 27, 350–360 (2001)

Bron C., Kerbosch J.: Finding all cliques of an undirected graph. Comm ACM 16, 575–577 (1973)

Canty M.J.: Resolving Conflicts with Mathematica: Algorithms for Two-Person Games. Academic Press, Amsterdam (2003)

Chvátal V.: Linear Programming. Freeman, New York (1983)

Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge, Mass (2001)

Dickhaut J., Kaplan T.: A program for finding Nash equilibria. Mathematica J 1(4), 87–93 (1991)

Fukuda K., Prodon A. et al.: Double description method revisited. In: Deza, M. (eds) Combinatorics and Computer Science, Lecture Notes in Computer Science, vol 1120., pp. 91–121. Springer, Berlin (1996)

Gilboa I., Zemel E.: Nash and correlated equilibria: some complexity considerations. Games Econ Behav 1, 80–93 (1989)

Jansen M.J.M.: Maximal Nash subsets for bimatrix games. Naval Res Logist Quart 28, 147–152 (1981)

Kohlberg E., Mertens J.-F.: On the strategic stability of equilibria. Econometrica 54, 1003–1037 (1986)

Kuhn H.W.: An algorithm for equilibrium points in bimatrix games. Proc Nat Acad Sci USA 47, 1657–1662 (1961)

Lemke C.E., Howson J.T. Jr: Equilibrium points of bimatrix games. J Soc Ind Appl Math 12, 413–423 (1964)

Mangasarian O.L.: Equilibrium points in bimatrix games. J Soc Ind Appl Math 12, 778–780 (1964)

McKelvey, R.D., McLennan, A.M., Turocy, T.L.: Gambit: Software Tools for Game Theory, Version 0.2007.01.30 http://econweb.tamu.edu/gambit (2007)

Millham C.B.: On Nash subsets of bimatrix games. Naval Res Logist Quart 21, 307–317 (1974)

Motzkin, T.S., Raiffa, H., Thompson, G.L., Thrall, R.M.: The double description method. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games II, pp. 51–73. Annals of Mathematics Studies 28, Princeton: Princeton University Press (1953)

Nash J.F.: Non-cooperative games. Ann Math 54, 286–295 (1951)

Rosenberg, G.D.: Enumeration of All Extreme Equilibria of Bimatrix Games with Integer Pivoting and Improved Degeneracy Check. CDAM Research Report LSE-CDAM-2005-18, London School of Economics (2005)

Savani, R.: Solve a bimatrix game. Interactive website. http://banach.lse.ac.uk/form.html (2005)

Shapley, L.S.: A note on the Lemke–Howson algorithm. Mathematical Programming Study 1: Pivoting and Extensions, pp. 175–189 (1974)

van den Elzen A.H., Talman A.J.J.: A procedure for finding Nash equilibria in bi-matrix games. Math Meth Oper Res 35, 27–43 (1991)

von Schemde A., von Stengel B.: Strategic characterization of the index of an equilibrium. In: Monien, B., Schroeder, U.-P. (eds) Symposium on Algorithmic Game Theory (SAGT) 2008, Lecture Notes in Computer Science, vol. 4997, pp. 242–254. Springer, Berlin (2008)

von Stengel B.: Efficient computation of behavior strategies. Games Econ Behav 14, 220–246 (1996)

von Stengel, B.: Improved equilibrium enumeration for bimatrix games. Extended Abstract, In: International Conference on Operations Research, ETH Zurich, 31 Aug–3 Sept. http://www.maths.lse.ac.uk/Personal/stengel/TEXTE/complement-enum.pdf (1998)

von Stengel B.: New maximal numbers of equilibria in bimatrix games. Discrete Comput Geom 21, 557–568 (1999)

von Stengel B.: Computing equilibria for two-person games. In: Aumann, R.J., Hart, S. (eds) Handbook of Game Theory, vol. 3., pp. 1723–1759. North-Holland, Amsterdam (2002)

Vorob’ev N.N.: Equilibrium points in bimatrix games. Theory Prob Appl 3, 297–309 (1958)

Winkels H.-M.: An algorithm to determine all equilibrium points of a bimatrix game. In: Moeschlin, O., Pallaschke, D. (eds) Game Theory and Related Topics., pp. 137–148. North-Holland, Amsterdam (1979)