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On the convergence of evolution processes with time-varying mutations and local interaction

Part of: Game theory Markov processes

Published online by Cambridge University Press:  14 July 2016

Hsiao-Chi Chen  and
Yunshyoung Chow
Hsiao-Chi Chen*
Affiliation:
National Taipei University
Yunshyoung Chow*
Affiliation:
Academia Sinica
*
∗ Postal address: Department of Economics, National Taipei University, 67, Section 3, Ming-Shen E. Road, Taipei 104, Taiwan, ROC. Email address: [email protected]
∗∗ Postal address: Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan, ROC.
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Abstract

This paper analyzes players’ long-run behavior in an evolutionary model with time-varying mutations under both uniform and local interaction rules. It is shown that a risk-dominant Nash equilibrium in a 2 × 2 coordination game would emerge as the long-run equilibrium if and only if mutation rates do not decrease to zero too fast under both interaction methods. The convergence rates of the dynamic system under both interaction rules are also derived. We find that the dynamic system with local matching may not converge faster than that with uniform matching.

Keywords

coordination gamecycle methodrisk-dominant equilibriuminhomogeneous Markov chaintime-varying mutations

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 91A22: Evolutionary games
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 301 - 323
Copyright
Copyright © Applied Probability Trust 2001 

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