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Adaptive play by idiosyncratic agents

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  • Myatt, David P.
  • Wallace, Chris C.

Abstract

Equilibrium selection in coordination games has generated a large literature. Kandori, Mailath and Rob (1993) and Young (1993) studied dynamic models of aggregate behaviour in which agents choose best responses to observations of population play. Crucially, infrequent mistakes (`mutations`) allow agents to take actions contrary to current trends and prevent initial configurations from determining long run play. An alternative approach is offered here: Harsanyian trembles are added to agents` payoffs so that with some probability it is optimal to act against the flow of play. The long run distribution of population behaviour is characterised - modes correspond to stable Bayesian Nash equilibria. Allowing the variance of payoff trembles to vanish, via a purification process, a single equilibrium is played almost always in the long run. Kandori et al and Young show that the number of contrarian actions required to escape an equilibrium determines selection; here, the likelihood that such actions are taken is of equal importance.
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Suggested Citation

  • Myatt, David P. & Wallace, Chris C., 2004. "Adaptive play by idiosyncratic agents," Games and Economic Behavior, Elsevier, vol. 48(1), pages 124-138, July.
    • Handle: RePEc:eee:gamebe:v:48:y:2004:i:1:p:124-138
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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, December.
    2. van Damme, E.E.C. & Weibull, J., 1998. "Evolution with Mutations Driven by Control Costs," Other publications TiSEM 197ad72d-2cb6-49c3-a875-e, Tilburg University, School of Economics and Management.
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    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    8. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
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    Citations

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    Cited by:

    1. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    2. Tom Quilter, 2007. "Noise Matters in Heterogeneous Populations," Edinburgh School of Economics Discussion Paper Series 169, Edinburgh School of Economics, University of Edinburgh.
    3. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    4. Myatt, David P. & Wallace, Chris, 2003. "A multinomial probit model of stochastic evolution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 286-301, December.
    5. Williams, Noah, 2022. "Learning and equilibrium transitions: Stochastic stability in discounted stochastic fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 145(C).
    6. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.
    7. Jean-Paul Carvalho, 2017. "Coordination and culture," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 449-475, October.
    8. Thomas Norman, "undated". "Step-by-Step Evolution with State-Dependent Mutations," Economics Papers 2003-W08, Economics Group, Nuffield College, University of Oxford.
    9. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
    10. Lahkar, Ratul, 2017. "Equilibrium selection in the stag hunt game under generalized reinforcement learning," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 63-68.
    11. Thomas Norman, 2010. "Cycles versus equilibrium in evolutionary games," Theory and Decision, Springer, vol. 69(2), pages 167-182, August.
    12. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    13. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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