Gradient-based algorithms for finding nash equilibria in extensive form games

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4858 LNCS, Issue , 2007, Pages 57-69

  Gilpin, Andrew ^a   Hoda, Samid ^b   Peña, Javier ^b   Sandholm, Tuomas ^a  

^a Carnegie Mellon University

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INFORMATION ANALYSIS; OPTIMIZATION; PROBLEM SOLVING; REAL TIME SYSTEMS;

NASH EQUILIBRIA; ZERO-SUM SEQUENTIAL GAMES;

GAME THEORY;

EID: 38449110214     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-77105-0_9     Document Type: Conference Paper

References (22)

1. Romanovskii, I.: Reduction of a game with complete memory to a matrix game. Soviet Mathematics 3, 678-681 (1962)
2. Koller, D., Megiddo, N.: The complexity of two-person zero-sum games in extensive form. Games and Economic Behavior 4(4), 528-552 (1992)
3. von Stengel, B.: Efficient computation of behavior strategies. Games and Economic Behavior 14(2), 220-246 (1996)
4. Koller, D., Pfeffer, A.: Representations and solutions for game-theoretic problems. Artificial Intelligence 94(1), 167-215 (1997) (Early version appeared in IJCAI-95)
5. Shi, J., Littman, M.: Abstraction methods for game theoretic poker. In: Computers and Games, Springer-Verlag, pp. 333-345. Springer, Heidelberg (2001)
6. Gilpin, A., Sandholm, T.: Lossless abstraction method for sequential games of imperfect information. Journal of the ACM (to appear) Early version appeared as Finding equilibria in large sequential games of imperfect information. In: Proceedings of the ACM Conference on Electronic Commerce (ACM-EC), Ann Arbor, MI, 2006 (2007)
7. Billings, D., Burch, N., Davidson, A., Holte, R., Schaeffer, J., Schauenberg, T., Szafron, D.: Approximating game-theoretic optimal strategies for full-scale poker. In: Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence (IJCAI), Acapulco, Mexico, pp. 661-668 (2003)
8. Gilpin, A., Sandholm, T.: A competitive Texas Hold'em poker player via automated abstraction and real-time equilibrium computation. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Boston, MA (2006)
9. Gilpin, A., Sandholm, T.: Better automated abstraction techniques for imperfect information games, with application to Texas Hold'em poker. In: International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), Honolulu, HI (2007)
10. Gilpin, A., Sandholm, T., Sørensen, T.B.: Potential-aware automated abstraction of sequential games, and holistic equilibrium analysis of Texas Hold'em poker. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), Vancouver, BC, Canada (2007)
11. Lipton, R.J., Young, N.E.: Simple strategies for large zero-sum games with applications to complexity theory. In: Proceedings of the Annual Symposium on Theory of Computing (STOC), Montreal, Quebec, Canada, pp. 734-740 (1994)
12. Lipton, R., Markakis, E., Mehta, A.: Playing large games using simple strategies. In: Proceedings of the ACM Conference on Electronic Commerce (ACM-EC), pp. 36-41. ACM Press, New York (2003)
13. Daskalakis, C., Mehta, A., Papadimitriou, C.: A note on approximate Nash equilibria. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, Springer, Heidelberg (2006)
14. Daskalakis, C., Mehta, A., Papadimitriou, C.: Progress in approximate Nash equilibria. In: Proceedings of the ACM Conference on Electronic Commerce (ACM-EC), pp. 355-358. ACM Press, New York (2007)
15. Feder, T., Nazerzadeh, H., Saberi, A.: Approximating Nash equilibria using small-support strategies. In: Proceedings of the ACM Conference on Electronic Commerce (ACM-EC), pp. 352-354. ACM Press, New York (2007)
16. Freund, Y., Schapire, R.: Adaptive game playing using multiplicative weights. Games and Economic Behavior 29, 79-103 (1999)
17. Nesterov, Y.: Excessive gap technique in nonsmooth convex minimization. SIAM Journal of Optimization 16(1), 235-249 (2005)
18. Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course. Kluwer Academic Publishers, Dordrecht (2004)
19. Lu, Z., Nemirovski, A., Monteiro, R.D.C.: Large-scale semidefinite programming via a saddle point mirror-prox algorithm. Mathematical Programming, Series B 109(2-3), 211-237 (2007)
20. Chudak, F.A., Eleutério, V.: Improved approximation schemes for linear programming relaxations of combinatorial optimization problems. In: Jünger, M., Kaibel, V. (eds.) Integer Programming and Combinatorial Optimization. LNCS, vol. 3509, pp. 81-96. Springer, Heidelberg (2005)
21. Hoda, S., Gilpin, A.: Peña, J.: A gradient-based approach for computing Nash equilibria of large sequential games (2007), Available at, http://www.optimization-online.org/
22. Billings, D., Davidson, A., Schaeffer, J., Szafron, D.: The challenge of poker. Artificial Intelligence 134(1-2), 201-240 (2002)