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Best-Response Dynamics In A Birth-Death Model Of Evolution In Games

Author

Listed:
  • CARLOS ALÓS-FERRER

    (Department of Economics, University of Konstanz, Box 150, D-78457 Konstanz, Germany)

  • ILJA NEUSTADT

    (Socioeconomic Institute, University of Zurich, Hottingerstrasse 10 CH-8032 Zurich, Switzerland)

Abstract

We consider a model of evolution with mutations as in Kandoriet al.(1993) [Kandori, M., Mailath, G.J., Rob, R., 1993. Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56], where agents follow best-response decision rules as in Sandholm (1998) [Sandholm, W., 1998. Simple and clever decision rules for a model of evolution. Economics Letters 61, 165–170]. Contrary to those papers, our model gives rise to a birth-death process, which allows explicit computation of the long-run probabilities of equilibria for given values of the mutation rate and the population size. We use this fact to provide a direct proof of the stochastic stability of risk-dominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.

Suggested Citation

  • Carlos Alós-Ferrer & Ilja Neustadt, 2010. "Best-Response Dynamics In A Birth-Death Model Of Evolution In Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 197-204.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:02:n:s021919891000260x
    DOI: 10.1142/S021919891000260X
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    Keywords

    Coordination games; learning; mutation; birth-death processes; C72; D83;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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