Brown's original fictitious play

Journal of Economic Theory

Volumn 135, Issue 1, 2007, Pages 572-578

  Berger, Ulrich ^a  

^a VIENNA UNIVERSITY OF ECONOMICS AND BUSINESS   (Austria)

Author keywords

Fictitious play; Learning process; Ordinal potential games

Indexed keywords

EID: 34250625767     PISSN: 00220531     EISSN: 10957235     Source Type: Journal    
DOI: 10.1016/j.jet.2005.12.010     Document Type: Article

References (32)

1. Berger U. Fictitious play in 2 × n games. J. Econ. Theory 120 (2005) 139-154
2. U. Berger, Two more classes of games with the continuous-time fictitious play property, Mimeo, Vienna University of Economics, 2005.
3. G.W. Brown, Some notes on computation of games solutions, Report P-78, The Rand Corporation, 1949.
4. Brown G.W. Iterative solution of games by fictitious play. In: Koopmans T.C. (Ed). Activity Analysis of Production and Allocation (1951), Wiley, New York 374-376
5. S. Cowan, Dynamical systems arising from game theory, Dissertation, UC Berkeley, 1992.
6. Cressman R. Evolutionary Dynamics and Extensive form Games (2003), MIT Press, Cambridge, MA
7. Foster D.P., and Young H.P. On the nonconvergence of fictitious play in coordination games. Games Econ. Behav. 25 (1998) 79-96
8. Fudenberg D., and Levine D.K. The Theory of Learning in Games (1998), MIT Press, Cambridge, MA
9. Gaunersdorfer A., and Hofbauer J. Fictitious play, Shapley polygons, and the replicator equation. Games Econ. Behav. 11 (1995) 279-303
10. Hahn S. The convergence of fictitious play in 3 × 3 games with strategic complementarities. Econ. Letters 64 (1999) 57-60
11. J. Hofbauer, Stability for the best response dynamics, Mimeo, University of Vienna, Viemma, 1995.
12. Hofbauer J., and Sigmund K. The Theory of Evolution and Dynamical Systems (1988), Cambridge University Press, Cambridge, UK
13. Hofbauer J., and Sigmund K. Evolutionary game dynamics. Bull. Amer. Math. Soc. 40 (2003) 479-519
14. Hon-Snir S., Monderer D., and Sela A. A learning approach to auctions. J. Econ. Theory 82 (1998) 65-88
15. Jordan J. Three problems in learning mixed-strategy Nash equilibria. Games Econ. Behav. 5 (1993) 368-386
16. Karlin S. Mathematical Methods and Theory in Games, Programming and Economics vol. 1 (1959), Addison-Wesley, Reading, MA
17. V. Krishna, Learning in games with strategic complementarities, Mimeo, Harvard University, Cambridge, MA 1992.
18. Krishna V., and Sjöström T. Learning in games: fictitious play dynamics. In: Hart S., and Mas-Colell A. (Eds). Cooperation: Game-theoretic Approaches (1997), Springer, Berlin
19. Krishna V., and Sjöström T. On the convergence of fictitious play. Math. Operations Res. 23 (1998) 479-511
20. Luce R.D., and Raiffa H. Games and Decisions (1957), Wiley, New York
21. McKinsey J.C. Introduction to the Theory of Games (1952), McGraw-Hill, New York
22. Milgrom P., and Roberts J. Adaptive and sophisticated learning in normal form games. Games Econ. Behav. 3 (1991) 82-100
23. K. Miyazawa, On the convergence of the learning process in a 2 × 2 non-zero-sum two-person game, Econometric Research Program, Princeton University, Research Memorandum No. 33, 1961.
24. Monderer D., and Sela A. A 2 × 2 game without the fictitious play property. Games Econ. Behav. 14 (1996) 144-148
25. D. Monderer, A. Sela, Fictitious play and no-cycling conditions, Mimeo, The Technion, 1997.
26. Monderer D., and Shapley L.S. Fictitious play property for games with identical interests. J. Econ. Theory 68 (1996) 258-265
27. Monderer D., and Shapley L.S. Potential games. Games Econ. Behav. 14 (1996) 124-143
28. Robinson J. An iterative method of solving a game. Ann. Math. 54 (1951) 296-301
29. Rosenthal R.W. A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2 (1973) 65-67
30. Sela A. Fictitious play in 2 × 3 games. Games Econ. Behav. 31 (2000) 152-162
31. Shapley L.S. Some topics in two-person games. Ann. Math. Stud. 5 (1964) 1-28
32. J. Szép, F. Forgó, Einführung in die Spieltheorie, Verlag Harri Deutsch, Thun, Frankfurt am Main, 1983.