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The Evolution of Coordination under Inertia

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  • Thomas Norman
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    Abstract

    This paper models the phenomenon of inertia driven by individual strategy switching costs in a stochastic evolutionary context. Kandori, Mailath, and Rob`s (1993) model of a finite population of agents repeatedly playing a 2x2 symmetric coordination game is extended to allow for such inertia. Taking noise to the limit, a number of new short- to medium-run equilibria emerge, centred around the mixed-strategy equilibrium. Thus, unusually, an evolutionary model is seen to provide some justification for the controversial concept of mixed-strategy equilibrium. However, Kandori, Mailath, and Rob`s long-run selection of the risk-dominant equilibrium continues to hold, both under fixed-rate mutations and under state-dependent mutations driven by stochastic switching costs. The key to this is the satisfaction of Blume`s (1999) skew-symmetry of the noise process, which is shown to be crucial even under simultaneous strategy revisions. In fact, the presence of the new short-run equilibria can under certain conditions serve to reduce the expected waiting time before the risk-dominant equilibrium is reached - an instance of Ellison`s (2000) idea that evolution is more rapid when it can proceed via a series of small steps between extremes. This suggests inertia to be a surprisingly efficient phenomenon, and also serves to moderate the force of the Ellison (1993) critique of excessively long transition times in models with vanishing noise.

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    File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W6/SpeedEctConf.pdf
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    Bibliographic Info

    Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2003-W06.

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    Date of creation: 01 Jan 2003
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    Handle: RePEc:oxf:wpaper:2003-w06

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    1. Lee, In Ho & Szeidl, Adam & Valentinyi, Akos, 2000. "Contagion and state dependent mutations," Discussion Paper Series In Economics And Econometrics 0027, Economics Division, School of Social Sciences, University of Southampton.
    2. Lipman, Barton L. & Wang, Ruqu, 2000. "Switching Costs in Frequently Repeated Games," Journal of Economic Theory, Elsevier, vol. 93(2), pages 149-190, August.
    3. Thomas Norman, 2003. "The Evolution of Conflict under Inertia," Economics Papers 2003-W07, Economics Group, Nuffield College, University of Oxford.
    4. Myatt, David P. & Wallace, Chris C., 2004. "Adaptive play by idiosyncratic agents," Games and Economic Behavior, Elsevier, vol. 48(1), pages 124-138, July.
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