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Evolution with Mutations Driven by Control Costs

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  • Eric Van Damme
  • Jorgen W Weibull

Abstract

Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive dynamics in Kandori, Mailath and Rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model these mutation rates as endogenously determined mistake probabilities, by assuming that players at some cost or disutility can control their mistake probability, i.e., the probability of implementing another pure strategy than intented. This is shown to corroborate the result in Kandori-Mailath-Rob and Young that the risk-dominant equilibrium is selected in 2 x 2-coordination games.
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Suggested Citation

  • Eric Van Damme & Jorgen W Weibull, 1999. "Evolution with Mutations Driven by Control Costs," Levine's Working Paper Archive 2113, David K. Levine.
  • Handle: RePEc:cla:levarc:2113
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, September.
    2. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    3. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
    4. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    8. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    9. Robles, Jack, 1998. "Evolution with Changing Mutation Rates," Journal of Economic Theory, Elsevier, vol. 79(2), pages 207-223, April.
    10. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
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    Cited by:

    1. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    2. Edward Droste & Robert P. Gilles & Cathleen Johnson, 2000. "Evolution of Conventions in Endogenous Social Networks," Econometric Society World Congress 2000 Contributed Papers 0594, Econometric Society.
    3. Kosfeld, Michael, 2002. "Why shops close again: An evolutionary perspective on the deregulation of shopping hours," European Economic Review, Elsevier, vol. 46(1), pages 51-72, January.
    4. Kosfeld, M., 1999. "Stochastic Strategy Adjustment in Coordination Games," Other publications TiSEM c676f553-60bf-4377-816c-7, Tilburg University, School of Economics and Management.
    5. Myatt, David P. & Wallace, Chris C., 2004. "Adaptive play by idiosyncratic agents," Games and Economic Behavior, Elsevier, vol. 48(1), pages 124-138, July.
    6. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
    7. Ivar Kolstad, 2005. "Evolution With Endogenous Mutations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 229-240.
    8. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    9. Nyborg, Karine & Telle, Kjetil, 2004. "The role of warnings in regulation: keeping control with less punishment," Journal of Public Economics, Elsevier, vol. 88(12), pages 2801-2816, December.

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    More about this item

    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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