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Stochastic imitative game dynamics with committed agents

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  • Sandholm, William H.

Abstract

We consider models of stochastic evolution in two-strategy games in which agents employ imitative decision rules. We introduce committed agents: for each strategy, we suppose that there is at least one agent who plays that strategy without fail. We show that unlike the standard imitative model, the model with committed agents generates unambiguous infinite horizon predictions: the asymptotics of the stationary distribution do not depend on the order in which the mutation rate and population size are taken to their limits.

Suggested Citation

  • Sandholm, William H., 2012. "Stochastic imitative game dynamics with committed agents," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2056-2071.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:2056-2071
    DOI: 10.1016/j.jet.2012.05.018
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    References listed on IDEAS

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    9. Sandholm, William H., 2007. "Simple formulas for stationary distributions and stochastically stable states," Games and Economic Behavior, Elsevier, vol. 59(1), pages 154-162, April.
    10. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    11. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
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    Cited by:

    1. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
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    3. Vassili Kolokoltsov, 2017. "The Evolutionary Game of Pressure (or Interference), Resistance and Collaboration," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 915-944, November.
    4. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, I: Theory," Center for Mathematical Economics Working Papers 505, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    Evolutionary game theory; Imitation; Committed agents; Stochastic stability; Equilibrium selection;
    All these keywords.

    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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