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Scale functions in equilibrium selection games

Author

Listed:
  • Madjid Amir

    (Institut for Statistics and Mathematical Economics, University of Karlsruhe, D-76128 Karlsruhe, Germany)

  • Siegfried Berninghaus

    (Institut for Statistics and Mathematical Economics, University of Karlsruhe, D-76128 Karlsruhe, Germany)

Abstract

We present here an evolutionary game model, and address the issue of equilibrium selection working with the scale function of a diffusion process describing the dynamics of population processes with mutation modeled as white noise. This model is the same as the one in Foster and Young (1990) but with a different interpretation at the boundaries and with different mutation modelings. First, we justifiably assume that the boundaries of the solution of the stochastic differential equation are absorbing so that the first boundary of the interval [0,1] hit will determine the equilibrium selected. Then, working with the scale function, we obtain for 2, 2 symmetric games and different mutation parameters, some new and interesting equilibrium selection results. The aim of this article is to describe another method of approach in evolutionary games with mutation which we believe will prove to be very useful in studying more general normal form games and different mutation modelings.

Suggested Citation

  • Madjid Amir & Siegfried Berninghaus, 1998. "Scale functions in equilibrium selection games," Journal of Evolutionary Economics, Springer, vol. 8(1), pages 1-13.
    • Handle: RePEc:spr:joevec:v:8:y:1998:i:1:p:1-13
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    More about this item

    Keywords

    Equilibrium selection ; Scale functions ; Stochastic evolutionary games;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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