Learning in games with unstable equilibria

Journal of Economic Theory

Volumn 144, Issue 4, 2009, Pages 1694-1709

  Benaïm, Michel ^a   Hofbauer, Josef ^b   Hopkins, Ed ^c  

^a UNIVERSITY OF NEUCHÂTEL   (Switzerland)

^b UNIVERSITY OF VIENNA   (Austria)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Best response dynamics; Games; Learning; Mixed strategy equilibria; Stochastic fictitious play; TASP

Indexed keywords

EID: 67649324906     PISSN: 00220531     EISSN: 10957235     Source Type: Journal    
DOI: 10.1016/j.jet.2008.09.003     Document Type: Article

References (42)

1. Anderson S., Goeree J., and Holt C. The logit equilibrium: A perspective on intuitive behavioral anomalies. Southern Econ. J. 69 (2002) 21-47
2. Benaïm M., and Hirsch M.W. Mixed equilibria and dynamical systems arising from fictitious play in perturbed games. Games Econ. Behav. 29 (1999) 36-72
3. M. Benaïm, J. Hofbauer, E. Hopkins, Learning in games with unstable equilibria, Working paper, University of Edinburgh, 2005
4. Benaïm M., Hofbauer J., and Sorin S. Stochastic approximation and differential inclusions. SIAM J. Control Optim. 44 (2005) 328-348
5. M. Benaïm, J. Hofbauer, S. Sorin, Stochastic approximation and differential inclusions, Part 3: Extensions, 2008
6. Benaïm M., and Weibull J. Deterministic approximation of stochastic evolution in games. Econometrica 71 (2003) 873-903
7. Benveniste A., Métivier M., and Priouret P. Adaptive Algorithms and Stochastic Approximations (1990), Springer-Verlag, Berlin
8. Brown J., and Rosenthal R. Testing the minimax hypothesis: A reexamination of O'Neill's game experiment. Econometrica 58 (1990) 1065-1081
9. Brown Kruse J., Rassenti S., Reynolds S.S., and Smith V.L. Bertrand-Edgeworth competition in experimental markets. Econometrica 62 (1994) 343-371
10. Burdett K., and Judd K. Equilibrium price dispersion. Econometrica 51 (1983) 955-969
11. Camerer C., and Ho T.-H. Experience-weighted attraction learning in normal form games. Econometrica 67 (1999) 827-874
12. Cason T., and Friedman D. Buyer search and price dispersion: A laboratory study. J. Econ. Theory 112 (2003) 232-260
13. Cason T., Friedman D., and Wagener F. The dynamics of price dispersion or Edgeworth variations. J. Econ. Dynam. Control 29 (2005) 801-822
14. Cheung Y.-W., and Friedman D. Individual learning in normal form games: Some laboratory results. Games Econ. Behav. 19 (1997) 46-76
15. Edgeworth F.Y. The pure theory of monopoly. Papers Relating to Political Economy, vol. 1 (1925), Burt Franklin, New York
16. Ellison G., and Fudenberg D. Learning purified mixed equilibria. J. Econ. Theory 90 (2000) 84-115
17. Foster D.P., and Young H.P. Learning, hypothesis testing, and Nash equilibrium. Games Econ. Behav. 45 (2003) 73-96
18. Fudenberg D., and Kreps D. Learning mixed equilibria. Games Econ. Behav. 5 (1993) 320-367
19. Fudenberg D., and Levine D. The Theory of Learning in Games (1998), MIT Press, Cambridge, MA
20. D. Fudenberg, S. Takahashi, Heterogeneous beliefs and local information in stochastic fictitious play, Working paper, 2007
21. Garay B., and Hofbauer J. Chain recurrence and discretization. Bull. Austral. Math. Soc. 55 (1997) 63-71
22. Gaunersdorfer A., and Hofbauer J. Fictitious play, Shapley polygons, and the replicator equation. Games Econ. Behav. 11 (1995) 279-303
23. Gilboa I., and Matsui A. Social stability and equilibrium. Econometrica 59 (1991) 859-867
24. Hart S., and Mas-Colell A. A simple adaptive procedure leading to correlated equilibrium. Econometrica 68 (2000) 1127-1150
25. J. Hofbauer, Stability for the best response dynamics, Working paper, University of Vienna, 1995
26. Hofbauer J. From Nash and Brown to Maynard Smith: Equilibria, dynamics and ESS. Selection 1 (2000) 81-88
27. Hofbauer J., and Hopkins E. Learning in perturbed asymmetric games. Games Econ. Behav. 52 (2005) 133-152
28. Hofbauer J., and Sandholm W.H. On the global convergence of stochastic fictitious play. Econometrica 70 (2002) 2265-2294
29. Hofbauer J., and Sandholm W.H. Evolution in games with randomly disturbed payoffs. J. Econ. Theory 132 (2005) 47-69
30. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge, UK
31. Hopkins E. Learning, matching and aggregation. Games Econ. Behav. 26 (1999) 79-110
32. Hopkins E. A note on best response dynamics. Games Econ. Behav. 29 (1999) 138-150
33. Hopkins E. Two competing models of how people learn in games. Econometrica 70 (2002) 2141-2166
34. Hopkins E., and Seymour R. The stability of price dispersion under seller and consumer learning. Int. Econ. Rev. 43 (2002) 1157-1190
35. McKelvey R.D., and Palfrey T.R. Quantal response equilibria for normal form games. Games Econ. Behav. 10 (1995) 6-38
36. Monderer D., and Shapley L.S. Fictitious play property for games with identical interests. J. Econ. Theory 68 (1996) 258-265
37. Morgan J., Orzen H., and Sefton M. An experimental study of price dispersion. Games Econ. Behav. 54 (2006) 134-158
38. Shapley L.S. Some topics in two person games. In: Dresher M., et al. (Ed). Advances in Game Theory (1964), Princeton University Press, Princeton
39. Stuart A.M., and Humphries A.R. Dynamical Systems and Numerical Analysis (1996), Cambridge University Press, Cambridge
40. Varian H.R. A model of sales. Amer. Econ. Rev. 70 (1980) 651-659
41. Viossat Y. The replicator dynamics does not lead to correlated equilibria. Games Econ. Behav. 59 (2007) 397-407
42. Young H.P. Strategic Learning and Its Limits (2004), Oxford University Press