Mixed-integer programming methods for finding Nash equilibria

Proceedings of the National Conference on Artificial Intelligence

Volumn 2, Issue , 2005, Pages 495-501

  Sandholm, Tuomas ^a   Gilpin, Andrew ^a   Conitzer, Vincent ^a  

^a Carnegie Mellon University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MIXED INTEGER PROGRAM (MIP); NASH FORMULATIONS; PORTER-NUDELMAN-SHOHAM (PNS);

ALGORITHMS; DATABASE SYSTEMS; GAME THEORY; INTEGER PROGRAMMING;

ARTIFICIAL INTELLIGENCE;

EID: 29344453416     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. Antipin, A. 2003. Extragradient approach to the solution of two person non-zero sum games. Optimization and Optimal Control, World Scientific. 1-28.
2. Aumann, R. 1959. Acceptable points in general cooperative n-person games, volume IV of Contributions to the Theory of Games. Princeton University Press.
3. Bernheim, B. D.; Peleg, B.; and Whinston, M. D. 1987. Coalition-proof Nash equilibria: I concepts. Journal of Economic Theory 42(1): 1-12.
4. Conitzer, V., and Sandholm, T. 2003. Complexity results about Nash equilibria. In IJCAI-03, 765-771.
5. Dickhaut, J., and Kaplan, T. 1991. A program for finding Nash equilibria. The Mathematica Journal 87-93.
6. Gilboa, I., and Zemel, E. 1989. Nash and correlated equilibria: Some complexity considerations. Games and Economic Behavior 1(1):80-93.
7. ILOG Inc. 2003. CPLEX 9.0 User's Manual.
8. Khamisov, O. 2003. A global optimization approach to solving equilibrium programming problems. Optimization and Optimal Control. World Scientific. 155-164.
9. Lemke, C., and Howson, J. 1964. Equilibrium points of bimatrix games. Journal of the Society of Industrial and Applied Mathematics 12:413-423.
10. Lipton, R.; Markakis, E.; and Mehta, A. 2003. Playing large games using simple strategies. In ACM-EC, 36-41.
11. Mangasarian, O. 1964. Equilibrium points in bimatrix games. Journal of the Society for Industrial and Applied Mathematics 12(4):778-780.
12. McKelvey, R. D.; McLennan, A. M.; and Turocy, T. L. 2004. Gambit: Software tools for game theory, version 0.97.1.5.
13. McLennan, A., and Berg, J. 2005. The asymptotic expected number of Nash equilibria of two player normal form games. Games and Economic Behavior. Forthcoming.
14. Myerson, R. 1991. Game Theory: Analysis of Conflict. Harvard University Press, Cambridge.
15. Nash, J. 1950. Equilibrium points in n-person games. Proc. of the National Academy of Sciences 36:48-49.
16. Nemhauser, G., and Wolsey, L. 1999. Integer and Combinatorial Optimization. John Wiley & Sons.
17. Nudelman, E.; Wortman, J.; Leyton-Brown, K.; and Shoham, Y. 2004. Run the GAMUT: A comprehensive approach to evaluating game-theoretic algorithms. In AAMAS-04.
18. Padberg, M., and Rinaldi, G. 1987. Optimization of a 532-city symmetric traveling salesman problem by branch and cut. Operations Research Letters 6:1-7.
19. Papadimitriou, C. 2001. Algorithms, games and the Internet. In STOC, 749-753.
20. Porter, R.; Nudelman, E.; and Shoham, Y. 2004. Simple search methods for finding a Nash equilibrium. In AAAI-04, 664-669.
21. Savani, R., and von Stengel, B. 2004. Exponentially many steps for finding a Nash equilibrium in a bimatrix game. In FOCS.