Computing pure strategy nash equilibria in compact symmetric games

Proceedings of the ACM Conference on Electronic Commerce

Volumn , Issue , 2010, Pages 63-72

  Ryan, Christopher Thomas ^a   Jiang, Albert Xin ^b   Leyton Brown, Kevin ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

game theory; rational generating functions; symmetric games

Indexed keywords

COMPACT REPRESENTATION; FIXED NUMBERS; NASH EQUILIBRIA; NP COMPLETE; PARAMETERIZED; PIECEWISE-LINEAR; POLYNOMIAL-TIME ALGORITHMS; RATIONAL GENERATING FUNCTIONS; SYMMETRIC GAMES; UTILITY FUNCTIONS;

ELECTRONIC COMMERCE; FUNCTION EVALUATION; PIECEWISE LINEAR TECHNIQUES; POWDERS; RATIONAL FUNCTIONS;

GAME THEORY;

EID: 77954721423     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1807342.1807352     Document Type: Conference Paper

References (31)

1. C. Àlvarez, J. Gabarró, and M. Serna. Pure Nash equilibria in games with a large number of actions. In MFCS: Proceedings of the International Symposium on Mathematical Foundations of Computer Science, pages 95-106, 2005.
2. E. Anshelevich, A. Dasgupta, J. Kleinberg, E. Tardos, T. Wexler, and T. Roughgarden. The price of stability for network design with fair cost allocation. In FOCS: Proceedings of the Annual IEEE Symposium on Foundations of Computer Science, volume 45, pages 295-305. IEEE COMPUTER SOCIETY PRESS, 2004.
3. A. Barvinok. A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Mathematics of Operations Research, 19(4):769-779, 1994.
4. A. Barvinok and K. M. Woods. Short rational generating functions for lattice point problems. Journal of the American Mathematical Society, 16(957-979), 2003.
5. N. A. R. Bhat and K. Leyton-Brown. Computing Nash equilibria of action-graph games. In UAI: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pages 35-42, 2004.
6. F. Brandt, F. Fischer, and M. Holzer. Symmetries and the complexity of pure Nash equilibrium. Journal of Computer and System Sciences, 75(3):163-177, 2009.
7. X. Chen and X. Deng. Settling the complexity of two-player Nash equilibrium. In FOCS: Proceedings of the Annual IEEE Symposium on Foundations of Computer Science, pages 261-272, 2006.
8. S. Cheng, D. Reeves, Y. Vorobeychik, and M. Wellman. Notes on equilibria in symmetric games. In AAMAS-04 Workshop on Game-Theoretic and Decision-Theoretic Agents, 2004.
9. C. Daskalakis, A. Fabrikant, and C. Papadimitriou. The game world is flat: The complexity of Nash equilibria in succinct games. In ICALP: Proceedings of the International Colloquium on Automata, Languages and Programming, pages 513-524, 2006.
10. C. Daskalakis, P. W. Goldberg, and C. H. Papadimitriou. The complexity of computing a Nash equilibrium. In STOC: Proceedings of the Annual ACM Symposium on Theory of Computing, pages 61-70, 2006.
11. C. Daskalakis and C. Papadimitriou. Computing pure Nash equilibria via Markov random fields. In ACM-EC: Proceedings of the ACM Conference on Electronic Commerce, pages 91-99, 2006.
12. C. Daskalakis and C. H. Papadimitriou. Three-player games are hard. In ECCC: Proceedings of the Electronic Colloquium on Computational Complexity, 2005, TR05-139.
13. C. Daskalakis, G. Schoenebeck, G. Valiant, and P. Valiant. On the complexity of Nash equilibria of Action-Graph Games. In SODA: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2009.
14. J. A. De Loera, R. Hemmecke, and M. Köppe. Pareto optima of multicriteria integer linear programs. INFORMS Journal on Computing, 21(1):39-48, 2009.
15. N. R. Devanur and R. Kannan. Market equilibria in polynomial time for fixed number of goods or agents. In FOCS: Proceedings of the Annual IEEE Symposium on Foundations of Computer Science, pages 45-53, 2008.
16. A. Fabrikant, C. Papadimitriou, and K. Talwar. The complexity of pure Nash equilibria. In STOC: Proceedings of the Annual ACM Symposium on Theory of Computing, pages 604-612, 2004.
17. G. Gottlob, G. Greco, and F. Scarcello. Pure Nash equilibria: Hard and easy games. Journal of Artificial Intelligence Research, 24:357-406, 2005.
18. A. Jiang and K. Leyton-Brown. Computing pure Nash equilibria in symmetric Action Graph Games. In AAAI: Proceedings of the AAAI Conference on Artificial Intelligence, pages 79-85, 2007.
19. S. Kakade, M. Kearns, J. Langford, and L. Ortiz. Correlated equilibria in graphical games. In ACM-EC: Proceedings of the ACM Conference on Electronic Commerce, pages 42-47, 2003.
20. M. Kearns, M. Littman, and S. Singh. Graphical models for game theory. In UAI: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pages 253-260, 2001.
21. M. Köppe, C. Ryan, and M. Queyranne. Rational Generating Functions and Integer Programming Games. Arxiv preprint arXiv:0809.0689, 2008.
22. E. Koutsoupias and C. Papadimitriou. Worst-case equilibria. Computer Science Review, 3(2):65-69, 2009.
23. E. Lawler and D. Wood. Branch-and-bound methods: A survey. Operations Research, 14(4):699-719, 1966.
24. R. Moore. Global optimization to prescribed accuracy. Computers & Mathematics with Applications, 21(6-7):25-39, 1991.
25. J. Nash. Non-cooperative games. Annals of Mathematics, 54(2):286-295, February 1951.
26. N. Nisan, T. Roughgarden, E. Tardos, and V. V. Vazirani. Algorithmic Game Theory. Cambridge University Press, 2007.
27. C. H. Papadimitriou and T. Roughgarden. Computing correlated equilibria in multi-player games. Journal of the ACM, 55(3):1-29, 2008.
28. R. Rosenthal. A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory, 2:65-67, 1973.
29. T. Roughgarden. Selfish routing and the price of anarchy. The MIT Press, 2005.
30. G. Schoenebeck and S. Vadhan. The computational complexity of Nash equilibria in concisely represented games. In ACM-EC: Proceedings of the ACM Conference on Electronic Commerce, pages 270-279, 2006.
31. K. Shoham and K. Leyton-Brown. Multiagent Systems: Algorithmic, Game-Theoretic and Logical Foundations. Cambridge University Press, 2009.