Enumeration of all the extreme equilibria in game theory: Bimatrix and polymatrix games

Journal of Optimization Theory and Applications

Volumn 129, Issue 3, 2006, Pages 349-372

  Audet, C ^a   Belhaiza, S ^b   Hansen, P ^c  

^a GERAD   (Canada)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^c HEC MONTRÉAL   (Canada)

Author keywords

Bimatrix games; Enumeration; Extreme equilibria; Nash equilibria; Polymatrix games

Indexed keywords

COMPUTATION THEORY;

BIMATRIX GAMES; ENUMERATION; EXTREME EQUILIBRIA; NASH EQUILIBRIA; POLYMATRIX GAME;

GAME THEORY;

EID: 33845609599     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-006-9070-3     Document Type: Article

References (27)

1. NASH, J. F., Equilibrium Points in n-Person Games, Proceedings of the National Academy of Sciences, Vol. 36, pp. 48-49, 1950.
2. MILLHAM, C. B., On Nash Subsets of Bimatrix Games, Naval Research Logistics Quarterly, Vol. 74, pp. 307-317, 1974.
3. AUDET, C., HANSEN, P., JAUMARD, B., and SAVARD, G., Enumeration of All Extreme Equilibrium Strategies of Bimatrix Games, SIAM Journal on Statistical and Scientific Computing, Vol. 23, pp. 323-338, 2001.
4. MILLS, H., Equilibrium Points in Finite Games, SIAM Journal on Applied Mathematics, Vol. 8, pp. 397-402, 1960.
5. MANGASARIAN, O. L., and STONE, H., Two-Person Nonzero-Sum Games and Quadratic Programming, Journal of Mathematical Analysis and Applications, Vol. 9, pp. 348-355, 1964.
6. MANGASARIAN, O. L., Equilibrium Points of Bimatrix Games, SIAM Journal on Applied Mathematics, Vol. 12, pp. 778-780, 1964.
7. VOROBEV, N. N., Equilibrium Points in Bimatrix Games, Theoriya Veroyatnostej i ee Primwneniya, Vol. 3, pp. 318-331, 1958
8. [English Version: Theory of Probability and Its Applications, Vol. 3, pp. 297-309, 1958].
9. KEIDING, H., On the Maximal Number of Nash Equilibria in a Bimatrix Game, Games and Economic Behavior, Vol. 21, pp. 148-160, 1997.
10. VON STENGEL, B., New Maximal Numbers of Equilibria in Bimatrix Games, Discrete and Computational Geometry, Vol. 21, pp. 557-568, 1998.
11. KUHN, H. W., An Algorithm for Equilibrium Points in Bimatrix Games, Proceedings of the National Academy of Sciences, Vol. 47, pp. 1657-1662, 1961.
12. LEMKE, C. E., and HOWSON, T. T., Equilibrium Points of Bimatrix Games, SIAM Journal on Applied Mathematics, Vol. 12, pp. 413-423, 1961.
13. DICKHAUT, J., and KAPLAN, T., A Program for Finding Nash Equilibria, Mathematica Journal, Vol. 1, pp. 87-93, 1991.
14. MCKELVEY, R. D., and MCLENNAN, A., Computation of Equilibria in Finite Games, Handbook of Computational Economics, Edited by H. M. Amman, D. A. Kendrick, and J. Rust, Elsevier, Amsterdam, Holland, Vol. 1, pp. 87-142, 1996.
15. WINKELS, R., An Algorithm to Determine all Equilibrium Points of a Bimatrix Games, Game Theory and Related Topics, Edited by O. Moeschlin and D. Pallaschke, North Holland Publishing Company, Amsterdam, Holland, 1972.
16. AUDET, C., Optimisation Globale Structurée: Proprié tés, Equivalences et Résolution, PhD Thesis, École Polytechnique de Montréal, pp. 91-109, 1997.
17. JÚDICE, J., and MITRA, G., Reformulations of Mathematical Programming Problems as Linear Complementarity Problems and Investigation of Their Solution Methods, Journal of Optimization Theory and Applications, Vol. 57, pp. 123-149, 1988.
18. AUDET, C., HANSEN, P., JAUMARD, B., and SAVARD, G., Links between Linear Bilevel and Mixed 0-1 Programming Problems, Journal of Optimization Theory and Applications, Vol. 93, pp. 273-300, 1997.
19. HOWSON, J. T., Equilibria of Polymatrix Games, Management Science, Vol. 18, pp. 312-318, 1972.
20. QUINTAS, L. G., A Note on Polymatrix Games, International Journal of Game Theory, Vols. 18-19, pp. 261-272, 1989.
21. COTTLE, R. W., and DANTZIG, G. B., Complementary Pivot Theory of Mathematical Programming, Mathematics of the Decision Scienes, Part 1, Vol. 11, pp. xxx-xxx, 1968.
22. YANOVSKAYA, E. B., Equilibrium Points in Polymatrix Games, Latvian Mathematical Collection, Vol. 8, pp. 381-384, 1968.
23. COTTLE, R. W., and DANTZIG, G. B., Linear Programming Extensions, Princeton University Press, Princeton, New Jersey, 1963.
24. LEMKE, C. E., Bimatrix Games Equilibrium Points and Mathematical Programming, Management Science, Vol. 11, pp.xxx-xxx, 1965.
25. EAVES, C. B., Polymatrix Games with Joint Constraints, SIAM Journal on Applied Mathematics, Vol. 24, pp. 418-423, 1973.
26. HOWSON, J. T., and ROSENTHAL, R. W., Bayesian Equilibria of Finite Two-Person Games with Incomplete Information, Management Science, Vol. 21, pp. 313-315, 1974.
27. MYERSON, R. B., Game Theory: Analysis of Conflict, Harvard University Press, Cambridge, Massachusetts, 1997.