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Boundedly rational quasi-Bayesian learning in coordination games with imperfect monitoring

Part of: Game theory Stochastic processes Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Hsiao-Chi Chen ,
Yunshyong Chow  and
June Hsieh
Hsiao-Chi Chen*
Affiliation:
National Taipei University
Yunshyong Chow*
Affiliation:
Academia Sinica, Taipei
June Hsieh*
Affiliation:
Academia Sinica, Taipei
*
∗Postal address: Department of Economics, National Taipei University, 67, Section 3, Min-Sheng E. Road, Taipei, Taiwan 104, Republic of China. Email address: [email protected]
∗∗∗Postal address: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, Republic of China.
∗∗∗Postal address: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, Republic of China.
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Abstract

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In this paper we study players' long-run behaviors in evolutionary coordination games with imperfect monitoring. In each time period, signals corresponding to players' underlying actions, instead of the actions themselves, are observed. A boundedly rational quasi-Bayesian learning process is proposed to extract information from the realized signals. We find that players' long-run behaviors depend not only on the correlations between actions and signals, but on the initial probabilities of risk-dominant and non-risk-dominant equilibria being chosen. The conditions under which risk-dominant equilibrium, non-risk-dominant equilibrium, and the coexistence of both equilibria emerges in the long run are shown. In some situations, the number of limiting distributions grows unboundedly as the population size grows to infinity.

Keywords

Coordination gamequasi-Bayesian learningimperfect monitoring

MSC classification

Primary: 91A22: Evolutionary games 60G99: None of the above, but in this section 60K99: None of the above, but in this section 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 335 - 350
Copyright
© Applied Probability Trust 2006 

Footnotes

Funding from the National Science Council (project no. NSC 92-2415-H-305-001) is gratefully acknowledged.

Funding from the National Science Council (project no. NSC 93-2115-M-001-011) is gratefully acknowledged.

References

Bergin, J. and Lipman, B. L. (1996). Evolution with state-dependent mutations. Econometrica 64, 943–956.CrossRefGoogle Scholar
Chen, H.-C. and Chow, Y. (2001). On the convergence of evolution processes with time-varying mutations and local interaction. J. Appl. Prob. 38, 301–323.CrossRefGoogle Scholar
Chen, H.-C. and Chow, Y. (2003). Equilibrium selection in coordination games with imperfect monitoring. Working paper, National Taipei University.Google Scholar
Compte, O. (2002). On failing to cooperate when monitoring is private. J. Econom. Theory 102, 151–188.CrossRefGoogle Scholar
Ellison, G. (1993). Learning, local interaction, and coordination. Econometrica 61, 1047–1071.CrossRefGoogle Scholar
Foster, D. and Young, P. (1990). Stochastic evolutionary game dynamics. Theoret. Pop. Biol. 38, 219–232.CrossRefGoogle Scholar
Fudenberg, D., Levine, D. and Maskin, E. (1994). The folk theorem with imperfect public information. Econometrica 62, 997–1039.CrossRefGoogle Scholar
Jordan, J. S. (1991). Bayesian learning in normal form games. Games Econom. Behavior 3, 60–81.CrossRefGoogle Scholar
Kalai, E. and Lehrer, E. (1993). Rational learning leads to Nash equilibrium. Econometrica 61, 1019–1045.CrossRefGoogle Scholar
Kandori, M. G., Mailath, G. J. and Rob, R. (1993). Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56.CrossRefGoogle Scholar
Mailath, G. J. and Morris, S. (2002). Repeated games with almost-public monitoring. J. Econom. Theory 102, 189–228.CrossRefGoogle Scholar
Robles, J. (1998). Evolution with changing mutation rates. J. Econom. Theory 79, 207–223.CrossRefGoogle Scholar
Robson, A. J. and Vega-Redondo, F. (1996). Efficient equilibrium selection in evolutionary games with random matching. J. Econom. Theory 70, 65–92.CrossRefGoogle Scholar
Sekiguchi, T. (1997). Efficiency in repeated prisoner's dilemma with private monitoring. J. Econom. Theory 76, 345–361.CrossRefGoogle Scholar
Young, H. P. (1993). The evolution of conventions. Econometrica 61, 57–84.CrossRefGoogle Scholar