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Equilibrium Selection in Evolutionary Games with Imperfect Monitoring

Part of: Markov processes Game theory

Published online by Cambridge University Press:  14 July 2016

Hsiao-Chi Chen  and
Yunshyong Chow
Hsiao-Chi Chen*
Affiliation:
National Taipei University
Yunshyong Chow*
Affiliation:
Academia Sinica
*
∗Postal address: Department of Economics, National Taipei University, 151 University Road, San-Shia, Taipei County 23741, Taiwan, R.O.C. Email address: [email protected]
∗∗Postal address: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, R.O.C. Email address: [email protected]
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Abstract

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In this paper we analyze players' long-run behavior in evolutionary coordination games with imperfect monitoring in a large population. Players can observe signals corresponding to other players' unseen actions and use the proposed simple or maximum likelihood estimation algorithm to extract information from the signals. In the simple learning process we find conditions for the risk-dominant and the non-risk-dominant equilibria to emerge alone in the long run. Furthermore, we find that the two equilibria can coexist in the long run. In contrast, the coexistence of the two equilibria is the only limit distribution under the maximum likelihood estimation learning algorithm. We also analyze the long-run equilibria of other 2x2 symmetric games under imperfect monitoring.

Keywords

Coordination gamerisk-dominant equilibriumimperfect monitoring

MSC classification

Secondary: 91A22: Evolutionary games 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 388 - 402
Copyright
Copyright © Applied Probability Trust 2008 

Footnotes

Funding from the National Science Council (project number: NSC 92-2415-H-305-001) is gratefully acknowledged. Valuable suggestions provided by an anonymous referee are also highly appreciated. Of course, all remaining errors belong to us.

Funding from the National Science Council in Taiwan is gratefully acknowledged.

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