On the Rate of Convergence of Fictitious Play

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)

   Google Scholar 

2. Berger, U.: Fictitious play in 2×n games. Journal of Economic Theory 120, 139–154 (2005)

   Article  MathSciNet  MATH  Google Scholar 

3. Berger, U.: Brown’s original fictitious play. Journal of Economic Theory 135, 572–578 (2007)

   Article  MathSciNet  MATH  Google Scholar 

4. Berger, U.: Learning in games with strategic complementarities revisited. Journal of Economic Theory 143, 292–301 (2008)

   Article  MathSciNet  MATH  Google Scholar 

5. Berger, U.: The convergence of fictitious play in games with strategic complementarities: A comment. MPRA Paper No. 20241, Munich Personal RePEc Archive (2009)

   Google Scholar 

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)

   Chapter  Google Scholar 

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)

   Google Scholar 

8. Conitzer, V.: Approximation guarantees for fictitious play. In: Proc. of 47th Annual Allerton Conference on Communication, Control and Computing (2009)

   Google Scholar 

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)

   Article  Google Scholar 

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)

    Google Scholar 

11. Fudenberg, D., Levine, D.: Universal consistency and cautious fictitious play. Journal of Economic Dynamics and Control 19, 1065–1089 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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)

    Google Scholar 

13. Gjerstad, S.: The rate of convergence of continuous fictitious play. Journal of Economic Theory 7, 161–178 (1996)

    Article  MathSciNet  MATH  Google Scholar 

14. Hahn, S.: The convergence of fictitious play in 3×3 games with strategic complementarities. Economic Letters 64, 57–60 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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)

    Google Scholar 

16. Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. John Wiley & Sons Inc., Chichester (1957)

    MATH  Google Scholar 

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)

    Google Scholar 

18. Monderer, D., Sela, A.: A 2×2 game without the fictitious play property. Games and Economic Behavior 14, 144–148 (1996)

    Article  MathSciNet  MATH  Google Scholar 

19. Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

20. Monderer, D., Shapley, L.S.: Fictitious play property for games with identical interests. Journal of Economic Theory 68, 258–265 (1996)

    Article  MathSciNet  MATH  Google Scholar 

21. Nachbar, J.H.: “Evolutionary” selection dynamics in games: Convergence and limit properties. International Journal of Game Theory 19, 59–89 (1990)

    Article  MathSciNet  MATH  Google Scholar 

22. Powers, R., Shoham, Y.: New criteria and a new algorithm for learning in multi-agent systems. In: Advances in Neural Information Processing Systems, vol. 17, pp. 1089–1096. MIT Press, Cambridge (2004)

    Google Scholar 

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)

    Google Scholar 

24. Robinson, J.: An iterative method of solving a game. Annals of Mathematics 54(2), 296–301 (1951)

    Article  MathSciNet  MATH  Google Scholar 

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)

    Google Scholar 

26. von Neumann, J.: Zur Theorie der Gesellschaftspiele. Mathematische Annalen 100, 295–320 (1928)

    Article  MathSciNet  Google Scholar 

27. von Neumann, J.: A numerical method to determine optimum strategy. Naval Research Logistics Quarterly 1(2), 109–115 (1954)

    Article  MathSciNet  Google Scholar 

28. Zhu, W., Wurman, P.R.: Structural leverage and fictitious play in sequential auctions. In: Proc. of 18th AAAI Conference, pp. 385–390 (2002)

    Google Scholar 

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