Equilibrium computation for two-player games in strategic and extensive form

Algorithmic Game Theory

Volumn 9780521872829, Issue , 2007, Pages 53-78

  von Stengel, Bernhard ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTER GAMES; TREES (MATHEMATICS);

CONDITION STATE; EQUATIONS AND INEQUALITIES; IMPERFECT INFORMATION; INFORMATION SET; NASH EQUILIBRIA; NON-COOPERATIVE GAME THEORY; SOLUTION CONCEPTS; TWO-PLAYER GAMES;

GAME THEORY;

EID: 84926118889     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511800481.005     Document Type: Chapter

References (34)

1. C. Audet, P. Hansen, B. Jaumard, and G. Savard. Enumeration of all extreme equilibria of bimatrix games. SIAM J. Sci. Comput.23, 323–338, 2001.
2. D. Avis and K. Fukuda. Apivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Disc. Comp. Geometry8, 295–313, 1992.
3. D. Avis. User’s Guide for lrs. Available at: http://cgm.cs.mcgill.ca/∼avis, 2005.
4. D.-O. Azulay and J.-F. Pique. A revised simplex method with integer Q-matrices. ACM Trans. Math. Software27, 350–360, 2001.
5. C. Bron and J. Kerbosch. Finding all cliques of an undirectred graph. Comm. ACM16, 575–577, 1973.
6. M.J. Canty. Resolving Conflict with Mathematica: Algorithms for Two-Person Games. Academic Press, Amsterdam, 2003.
7. R.S. Datta. Using computer algebra to compute Nash equilibria. Proc. 2003 Int. Symp. Symbolic and Algebraic Computation, ACM, 74–79, 2003.
8. J. Dickhaut and T. Kaplan. A program for finding Nash equilibria. Math. J.1:4, 87–93, 1991.
9. M.J.M. Jansen. Maximal Nash subsets for bimatrix games. Naval Res. Logistics Q.28, 147–152, 1981.
10. H. Keiding. On the maximal number of Nash equilibria in an n × n bimatrix game. Games Econ. Behav.21, 148–160, 1997.
11. D. Koller and N. Megiddo. The complexity of two-person zero-sum games in extensive form. Games Econ. Behav.4, 528–552, 1992.
12. D. Koller, N. Megiddo, and B. von Stengel. Efficient computation of equilibria for extensive twoperson games. Games Econ. Behav.14, 247–259, 1996.
13. H.W. Kuhn. Extensive games and the problem of information. In: Contributions to the Theory of Games II, eds. H. W. Kuhn and A. W. Tucker, Ann. Math. Studies 28, Princeton Univ. Press, Princeton, 193–216, 1953.
14. H.W. Kuhn. An algorithm for equilibrium points in bimatrix games. Proc. National Academy of Sciences of the U.S.A.47, 1657–1662, 1961.
15. C.E. Lemke. Bimatrix equilibrium points and mathematical programming. Manag. Sci.11, 681–689, 1965.
16. C.E. Lemke and J.T. Howson, Jr. Equilibrium points of bimatrix games. J. SIAM12, 413–423, 1964.
17. O.L. Mangasarian. Equilibrium points in bimatrix games. J. SIAM12, 778–780, 1964.
18. R.D. McKelvey, A. McLennan, and T.L. Turocy. Gambit: Software Tools for Game Theory. Available at: http://econweb.tamu.edu/gambit, 2006.
19. P. McMullen. The maximum number of faces of a convex polytope. Mathematika17, 179–184, 1970.
20. J.F. Nash. Non-cooperative games. Ann. Math.54, 286–295, 1951.
21. I.V. Romanovskii. Reduction of a game with complete memory to a matrix game. Soviet Math. 3, 678–681, 1962.
22. G.D. Rosenberg. Enumeration of all extreme equilibria of bimatrix games with integer pivoting and improved degeneracy check. CDAM Res. Rep. LSE-CDAM-2005-18, London School of Economics, 2004.
23. R. Savani and B. von Stengel. Hard-to-solve bimatrix games. Econometrica74, 397–429, 2006.
24. R. Selten. Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory4, 22–55, 1975.
25. L.S. Shapley. Anote on the Lemke–Howson algorithm. Mathematical Programming Study 1: Pivoting and Extensions, 175–189, 1974.
26. E. van Damme. Stability and Perfection of Nash Equilibria. Springer, Berlin, 1987.
27. A. von Schemde. Index and Stability in Bimatrix Games. Springer, Berlin, 2005.
28. B. von Stengel. Efficient computation of behavior strategies. Games Econ. Behav.14, 220–246, 1996.
29. B. von Stengel. New maximal numbers of equilibria in bimatrix games. Disc. Comp. Geometry21, 557–568, 1999.
30. B. von Stengel. Computing equilibria for two-person games. In: Handbook of Game Theory with Economic Applications, eds. R.J. Aumann and S. Hart, Elsevier, Amsterdam, 3, 1723–1759, 2002.
31. B. von Stengel, A.H. van den Elzen, and A.J.J. Talman. Computing normal form perfect equilibria for extensive two-person games. Econometrica70, 693–715, 2002.
32. N.N. Vorob’ev. Equilibrium points in bimatrix games. Theory of Probability and its Applications3, 297–309, 1958.
33. H.-M. Winkels. An algorithm to determine all equilibrium points of a bimatrix game. In: Game Theory and Related Topics, eds. O. Moeschlin and D. Pallaschke, North-Holland, Amsterdam, 137–148, 1979.
34. G.M. Ziegler. Lectures on Polytopes. Springer, New York, 1995.