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Evolutionary prisoner's dilemma games with one-dimensional local interaction and imitation

Part of: Markov processes Game theory

Published online by Cambridge University Press:  01 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 explore the impact of imitation rules on players' long-run behaviors in evolutionary prisoner's dilemma games. All players sit sequentially and equally spaced around a circle. Players are assumed to interact only with their neighbors, and to imitate either their successful neighbors and/or themselves or the successful actions taken by their neighbors and/or themselves. In the imitating-successful-player dynamics, full defection is the unique long-run equilibrium as the probability of players' experimentations (or mutations) tend to 0. By contrast, full cooperation could emerge in the long run under the imitating-successful-action dynamics. Moreover, it is discovered that the convergence rate to equilibrium under local interaction could be slower than that under global interaction.

Keywords

Cooperationimitationlocal interactionlong-run equilibriumprisoner's dilemma game

MSC classification

Primary: 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
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 1 , March 2009 , pp. 154 - 176
Copyright
Copyright © Applied Probability Trust 2009 

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