Social learning in recurring games. (English) Zbl 0891.90186
Games Econ. Behav. 21, No. 1-2, 102-134 (1997); erratum ibid. 25, No. 1, 145 (1998).
Summary: In a recurring game, a stage game is played sequentially by different groups of players. Each group receives publicly available information about the play of earlier groups. Not knowing the population distribution of player types (representing individual preferences and behavior), society members start with a prior probability distribution over a set of possible type-distributions. Late groups update their beliefs by considering the public information regarding the play of earlier groups. We study the limit beliefs and play of late groups and the relationships to the true (realized) type-distribution and equilibria of the true Bayesian stage game.
MSC:
| 91A20 | Multistage and repeated games |
References:
| [1] | Abreu, D.; Pearce, D.; Stacchetti, E., Optimal Cartel Equilibria with Imperfect Monitoring, Journal of Economic Theory, 39, 251-269 (1986) · Zbl 0606.90019 |
| [2] | Aumann, R. J., Irrationality in Game Theory, Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn (1992), MIT Press: MIT Press Cambridge, p. 214-227 |
| [3] | Aumann, R. J.; Hart, S., Handbook of Game Theory, with Economic Applications (1992), North-Holland: North-Holland Amsterdam · Zbl 0899.90166 |
| [4] | Aumann, R. J.; Maschler, M., Repeated Games with Incomplete Information: A Survey of Recent Results, Mathematica, 116, 287-403 (1967) |
| [5] | Aumann, R. J.; Maschler, M., Repeated Games with Incomplete Information (1995), MIT Press: MIT Press Cambridge · Zbl 0972.91501 |
| [6] | Banerjee, A., A Simple Model of Herd Behavior, Quart. J. Econ, 107, 797-817 (1992) |
| [7] | Bikhchandani, S.; Hirshleifer, D., A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades, J. Polit. Econ., 100, 992-1026 (1992) |
| [8] | Battigalli, P.; Gilli, M.; Molinari, M. C., Learning and Convergence to Equilibrium in Repeated Strategic Interactions: An Introductory Survey, Richerche Econ., 96, 335-378 (1992) · Zbl 0772.90093 |
| [9] | Blackwell, D.; Dubins, L., Merging of Opinions with Increasing Information, Ann. Math. Statist., 38, 882-886 (1962) · Zbl 0109.35704 |
| [11] | Fudenberg, D.; Kreps, D., Learning in Extensive Form Games, I. Self Confirming Equilibria, Games and Econ. Behav., 8, 20-55 (1994) · Zbl 0827.90144 |
| [12] | Fudenberg, D.; Levine, D., Self-Confirming Equilibrium, Econometrica, 61, 523-545 (1993) · Zbl 0796.90072 |
| [13] | Fudenberg, D.; Levine, D., Steady State Learning and Nash Equilibrium, Econometrica, 61, 547-573 (1993) · Zbl 0792.90096 |
| [14] | Fudenberg, D.; Tirole, J., Perfect Bayesian Equilibrium and Sequential Equilibrium, J. Econ. Theory, 53, 236-260 (1991) · Zbl 0717.90108 |
| [15] | Harsanyi, J. C., Games of Incomplete Information Played by Bayesian Players, Parts I-III, Managment Science, 14, 159-182 (1967-1968) · Zbl 0207.51102 |
| [16] | Jackson, M.; Kalai, E., Recurring Bullies, Trembling, and Learning, (Albers, W.; Guth, W.; Hammerstein, P.; Moldavanu, B.; van Damme, E., Understanding Strategic Interaction: Essays in Honor of Reinhard Selten (1995), Springer-Verlag: Springer-Verlag Berlin), 171-184 · Zbl 0876.90106 |
| [18] | Jordan, J., Bayesian Learning in Normal FormGames, Games Econ. Behav., 3, 60-81 (1991) · Zbl 0751.90087 |
| [19] | Jordan, J., Three Problems in Learning Mixed-Strategy Equilibria, Games Econ. Behav., 5, 368-386 (1993) · Zbl 0805.90131 |
| [20] | Kalai, E.; Lehrer, E., Rational Learning Leads to Nash Equilibrium, Econometrica, 61, 1019-1045 (1993) · Zbl 0793.90106 |
| [21] | Kalai, E.; Lehrer, E., Subjective Equilibrium in Repeated Games, Econometrica, 61, 1231-1240 (1993) · Zbl 0784.90110 |
| [22] | Kalai, E.; Lehrer, E., Weak and Strong Merging of Opinions, J. Math. Econ., 23, 73-86 (1994) · Zbl 0789.90022 |
| [23] | Kandori, M.; Mailath, G.; Rob, R., Learning, Mutation, and Long Run Equilibria, Econometrica, 61, 27-56 (1993) · Zbl 0776.90095 |
| [24] | Kreps, D.; Milgrom, P.; Roberts, D. J.; Wilson, R., Rational Cooperation in the Finitely-Repeated Prisoners’ Dilemma, J. Econ. Theory, 27, 245-252 (1982) · Zbl 0485.90092 |
| [25] | Lehrer, E., Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-Observable Actions, Int. J. Game Theory, 18, 57-89 (1989) · Zbl 0675.90109 |
| [26] | Lehrer, E.; Smorodinsky, R., Repeated Large Games with Incomplete Information, Games Econ. Behav., 18, 116-134 (1997) · Zbl 0889.90175 |
| [28] | Nachbar, J., Prediction, Optimization, and Rational Learning in Games, Econometrica, 275-310 (1997) · Zbl 0872.90126 |
| [29] | Nyarko, Y., Convergence in Economic Models with Bayesian Hierarchies of Beliefs, J. Econ. Theory (1996) |
| [31] | Radner, R., Collusive Behavior in Noncooperative Epsilon-Equilibrium of Oligopolies with Long but Finite Lives, J. Econ. Theory, 22, 136-154 (1980) · Zbl 0434.90015 |
| [32] | Sandroni, A., The Almost Absolute Continuity Hypothesis, Games Econ. Behav., 19 (1997) |
| [33] | Selten, R., Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Int. J. Game Theory, 4, 25-55 (1975) · Zbl 0312.90072 |
| [34] | Shapley, L. S., Stochastic Games, Proc. Nat. Acad. Sci. USA, 39, 327-332 (1953) · Zbl 0051.35805 |
| [36] | van Damme, E., Stability and Perfection of Nash Equilbria (1987), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0696.90087 |
| [38] | Young, P., The Evolution of Conventions, Econometrica, 61, 57-84 (1993) · Zbl 0773.90101 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
