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Strictly Dominated Strategies in the Replicator-Mutator Dynamics

  • Segismundo S. Izquierdo

    ()

    (Department of Industrial Organization, Universidad de Valladolid, Valladolid, 47011 Spain
    Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain)

  • Luis R. Izquierdo

    ()

    (Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain
    Department of Civil Engineering, Universidad de Burgos, Burgos, 09001 Spain)

The replicator-mutator dynamics is a set of differential equations frequently used in biological and socioeconomic contexts to model evolutionary processes subject to mutation, error or experimentation. The replicator-mutator dynamics generalizes the widely used replicator dynamics, which appears in this framework as the extreme case where replication is perfectly precise. This paper studies the influence of strictly dominated strategies on the location of the rest points of the replicator-mutator dynamics, at the limit where the mutation terms become arbitrarily small. It can be proved that such limit rest points for small mutation are Nash equilibria, so strictly dominated strategies do not occur at limit stationary points. However, we show through a simple case how strictly dominated strategies can have an influence on the location of the limit rest points for small mutation. Consequently, the characterization of the limit rest points of the replicator-mutator dynamics cannot in general proceed safely by readily eliminating strictly dominated strategies.

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Article provided by MDPI, Open Access Journal in its journal Games.

Volume (Year): 2 (2011)
Issue (Month): 3 (September)
Pages: 355-364

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Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:355-364:d:13950
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  1. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  2. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  3. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
  4. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  5. Sandholm, William H. & Hofbauer, Josef, 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
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