The complexity of finding nash equilibria

Algorithmic Game Theory

Volumn 9780521872829, Issue , 2007, Pages 29-52

  Papadimitriou, Christos H ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER GAMES;

ALGORITHMIC GAME THEORY; COMPLEXITY CLASS; CORRELATED EQUILIBRIA; NASH EQUILIBRIA; NORMAL FORM; QUIESCENT STATE; STRATEGIC BEHAVIOR;

GAME THEORY;

EID: 84926102360     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511800481.004     Document Type: Chapter

References (28)

1. T. Abbott, D. Kane, and P. Valiant. On the complexity of two-player win-lose games. Proc.2005FOCS
2. R.J. Aumann. Subjectivity and correlation in randomized strategies. J. Math. Econ., 1:67–96, 1974.
3. P. Beame, S. Cook, J. Edmonds, R. Impagliazzo, and T. Pitassi. The relative complexity of NP search problems. J. Comput. Syst. Sci., 57(1):13–19, 1998.
4. X. Chen and X. Deng. 3-NASH is PPAD-Complete. Electronic Colloquium on Computational Complexity, 134, 2005a.
5. X. Chen and X. Deng. Settling the complexity of 2-player Nash-equilibrium. Electronic Colloquium on Computational Complexity, 134, 2005b; Fdns. Comp. 2006, to appear.
6. X. Chen, X. Deng, and S. Teng. ComputingNash equilibria: Aprroximation and smoothed complexity. FOCS 2006, pp. 603–612, 2006.
7. B. Codenotti, M. Leoncini, and G. Resta. Efficient computation of Nash equilibria for very sparse win-lose games. Electronic Colloquium on Computational Complexity, 12, 2006.
8. V. Conitzer and T. Sandholm. Complexity results about Nash equilibria. In: Proc. 18th Int. Joint Conf. Artificial Intelligence, pp. 765–771, 2003.
9. C. Daskalakis, P.W. Goldberg, and C.H. Papadimitriou. The complexity of computing a Nash equilibrium. Symp. on Theory of Computing, 2006, pp. 71–78.
10. C. Daskalakis, A. Mehta, and C.H. Papadimitriou. A note on approximate Nash equilibria. In: Proc. 2006 Workshop on Internet Network Economics, in press.
11. C. Daskalakis and C.H. Papadimitriou. Three-player Games are Hard. Electronic Colloquium on Computational Complexity, 139, 2005.
12. F.S. Evangelista and T.E.S. Raghavan. A note on correlated equilibrium. Intl. J. Game Theory, 25(1):35–41, 2005.
13. D. Gale, H.W. Kuhn, and A.W. Tucker. On symmetric games. In: H.W. Kuhn and A.W. Tucker, editors, Contributions to the Theory Games, 1:81–87. Princeton University Press, 1950.
14. M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NPCompleteness, Freeman, 1979.
15. I. Gilboa and E. Zemel. Nash and correlated equilibria: Some complexity considerations. Games Econ. Behav., 1989.
16. P.W. Goldberg and C.H. Papadimitriou. Reducibility between equilibrium problems. Symp. on Theory of Computing, 2006, pp. 62–70.
17. S. Hart and D. Schmeidler. Existence of correlated equilibria. Math. Operat. Res., 14(1):18–25, 1989.
18. M. Hirsch, C.H. Papadimitriou, and S. Vavasis. Exponential lower bounds for finding brouwer fixpoints. J. Complexity, 5:379–416, 1989.
19. D.S. Johnson, C.H. Papadimitriou, and M. Yannakakis. How easy is local search? J. Comput. Syst. Sci., 37(1):79–100, 1988.
20. M. Kearns, M. Littman, and S. Singh. Graphical models for game theory. In: Proc. Conf. on Uncertainty in Artificial Intelligence, 2001, pp. 253–260.
21. K. Leyton-Brown and M. Tennenholtz. Local-effect games. Intl. Joint Conf. Artificial Intelligence, 2003, pp. 772–780.
22. R.J. Lipton, E. Markakis, and A. Mehta. Playing large games using simple strategies. ACMElectronic Commerce, 2003, pp. 36–41.
23. J. Nash. Noncooperative games. Ann. Math., 54:289–295, 1951.
24. C.H. Papadimitriou. On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. Syst. Sci., 48(3):498–532, 1994.
25. C.H. Papadimitriou. Computing correlated equilibria in multi-player games. Symp. on Theory of Computing, 2005, pp. 49–56.
26. C.H. Papadimitriou and T. Roughgarden. Computing equilibria in multi-player games. Symp. on Discrete Algorithms, 2005, pp. 82–91.
27. R. Savani and B. von Stengel. Exponentially many steps for finding a Nash equilibrium in a Bimatrix Game. Proc. of 45th Fdns. on Comp. Science, pp. 258–267, 2004.
28. B. von Stengel. Computing equilibria for two-person games. Handbook of Game Theory with Economic Applications, Vol. 3, R. J. Aumann and S. Hart, eds. Elsevier, Amsterdam, pp. 1723–1759, 2002.