On the rate of convergence of fictitious play

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

Volumn 6386 LNCS, Issue M4D, 2010, Pages 102-113

  Brandt, Felix ^a   Fischer, Felix ^b   Harrenstein, Paul ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEST RESPONSE; CONSTANT-SUM GAME; EXPONENTIAL NUMBERS; FICTITIOUS PLAY; MIXED STRATEGY; N-GAMES; NASH EQUILIBRIA; NASH EQUILIBRIUM; POTENTIAL GAMES; RATE OF CONVERGENCE; SIMPLE LEARNING ALGORITHMS; STRATEGIC GAME;

AD HOC NETWORKS; APPROXIMATION THEORY; LEARNING ALGORITHMS; TELECOMMUNICATION NETWORKS;

GAME THEORY;

EID: 78649597115     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-16170-4_10     Document Type: Conference Paper

References (28)

1. Bellman, R.: On a new iterative algorithm for finding the solutions of games and linear programming problems. In: Research Memorandum P-473, The RAND Corporation (1953)
2. Berger, U.: Fictitious play in 2×n games. Journal of Economic Theory 120, 139-154 (2005)
3. Berger, U.: Brown's original fictitious play. Journal of Economic Theory 135, 572-578 (2007)
4. Berger, U.: Learning in games with strategic complementarities revisited. Journal of Economic Theory 143, 292-301 (2008)
5. Berger, U.: The convergence of fictitious play in games with strategic complementarities: A comment. MPRA Paper No. 20241, Munich Personal RePEc Archive (2009)
6. Brandt, F., Fischer, F.: On the hardness and existence of quasi-strict equilibria. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 291-302. Springer, Heidelberg (2008)
7. Brown, G. W.: Iterative solutions of games by fictitious play. In: Koopmans, T. C. (ed.) Activity Analysis of Production and Allocation, pp. 374-376. John Wiley and Sons, Inc., Chichester (1951)
8. Conitzer, V.: Approximation guarantees for fictitious play. In: Proc. of 47th Annual Allerton Conference on Communication, Control and Computing (2009)
9. Conitzer, V., Sandholm, T.: AWESOME: A general multiagent learning algorithm that converges in self-play and learns a best response against stationary opponents. Machine Learning 67 (1-2), 23-43 (2007)
10. Dantzig, G. B.: A proof of the equivalence of the programming problem and the game problem. In: Koopmans, T. C. (ed.) Activity Analysis of Production and Allocation, pp. 330-335. John Wiley & sons Inc., Chichester (1951)
11. Fudenberg, D., Levine, D.: Universal consistency and cautious fictitious play. Journal of Economic Dynamics and Control 19, 1065-1089 (1995)
12. Ganzfried, S., Sandholm, T.: Computing an approximate jam/fold equilibrium for 3-player no-limit texas hold'em tournaments. In: Proc. of 7th AAMAS Conference, pp. 919-925 (2008)
13. Gjerstad, S.: The rate of convergence of continuous fictitious play. Journal of Economic Theory 7, 161-178 (1996)
14. Hahn, S.: The convergence of fictitious play in 3 × 3 games with strategic complementarities. Economic Letters 64, 57-60 (1999)
15. Hannan, J.: Approximation to Bayes risk in repeated plays. In: Dresher, M., Tucker, A. W., Wolfe, P. (eds.) Contributions to the Theory of Games, vol. 3, pp. 97-139. Princeton University Press, Princeton (1957)
16. Luce, R. D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. John Wiley & sons Inc., Chichester (1957)
17. Miyasawa, K.: On the convergence of the learning process in a 2 × 2 nonzero sum two-person game. In: Research Memorandum 33, Econometric Research Program. Princeton University, Princeton (1961)
18. Monderer, D., Sela, A.: A 2 × 2 game without the fictitious play property. Games and Economic Behavior 14, 144-148 (1996)
19. Monderer, D., Shapley, L. S.: Potential games. Games and Economic Behavior 14(1), 124-143 (1996)
20. Monderer, D., Shapley, L. S.: Fictitious play property for games with identical interests. Journal of Economic Theory 68, 258-265 (1996)
21. Nachbar, J. H.: "Evolutionary" selection dynamics in games: Convergence and limit properties. International Journal of Game Theory 19, 59-89 (1990)
22. Powers, R., Shoham, Y.: New criteria and a new algorithm for learning in multiagent systems. In: Advances in Neural Information Processing Systems, vol. 17, pp. 1089-1096. MIT Press, Cambridge (2004)
23. Rabinovich, Z., Gerding, E., Polukarov, M., Jennings, N. R.: Generalised fictitious play for a continuum of anonymous players. In: Proc. of 21st IJCAI, pp. 245-250 (2009)
24. Robinson, J.: An iterative method of solving a game. Annals of Mathematics 54(2), 296-301 (1951)
25. Shapley, L.: Some topics in two-person games. In: Dresher, M., Shapley, L. S., Tucker, A. W. (eds.) Advances in Game Theory. Annals of Mathematics Studies, vol. 52, pp. 1-29. Princeton University Press, Princeton (1964)
26. von Neumann, J.: Zur Theorie der Gesellschaftspiele. Mathematische Annalen 100, 295-320 (1928)
27. von Neumann, J.: A numerical method to determine optimum strategy. Naval Research Logistics Quarterly 1(2), 109-115 (1954)
28. Zhu, W., Wurman, P. R.: Structural leverage and fictitious play in sequential auctions. In: Proc. of 18th AAAI Conference, pp. 385-390 (2002)