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Contagion and State Dependent Mutations

Author

Listed:
  • Lee In Ho

    () (Seoul National University and University of Southampton)

  • Szeidl Adam

    () (Harvard University)

  • Valentinyi Akos

    () (University of Southampton, Institute of Economics, Hungarian Academy of Sciences & CEPR)

Abstract

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected in the long run under the best-response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size, the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest response is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for any given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exist only in local interaction settings and favor the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theory.

Suggested Citation

  • Lee In Ho & Szeidl Adam & Valentinyi Akos, 2003. "Contagion and State Dependent Mutations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-29, February.
  • Handle: RePEc:bpj:bejtec:v:advances.3:y:2003:i:1:n:2
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    References listed on IDEAS

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    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
    3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. 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.
    7. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    8. Anderlini, Luca & Ianni, Antonella, 1996. "Path Dependence and Learning from Neighbors," Games and Economic Behavior, Elsevier, vol. 13(2), pages 141-177, April.
    9. In Ho Lee & Akos Valentinyi, 2000. "Noisy Contagion Without Mutation," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 47-56.
    10. Stephen Morris, 2000. "Contagion," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 57-78.
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    Citations

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    Cited by:

    1. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-1002-3 is not listed on IDEAS
    2. Azomahou, T. & Opolot, D., 2014. "Epsilon-stability and the speed of learning in network games," MERIT Working Papers 036, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    3. Weidenholzer, Simon, 2012. "Long-run equilibria, dominated strategies, and local interactions," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1014-1024.
    4. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    5. Azomahou, T. & Opolot, D., 2014. "Stability and strategic diffusion in networks," MERIT Working Papers 035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    6. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 1-35, November.
    7. Thomas Norman, "undated". "Step-by-Step Evolution with State-Dependent Mutations," Economics Papers 2003-W08, Economics Group, Nuffield College, University of Oxford.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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