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Stochastic imitative game dynamics with committed agents

  • Sandholm, William H.
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    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.

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    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 147 (2012)
    Issue (Month): 5 ()
    Pages: 2056-2071

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    Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:2056-2071
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    1. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
    2. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    5. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    6. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    7. Sandholm, William H., 2010. "Orders of limits for stationary distributions, stochastic dominance, and stochastic stability," Theoretical Economics, Econometric Society, vol. 5(1), January.
    8. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994.
    9. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    10. Imhof, Lorens & Fudenberg, Drew, 2008. "Monotone Imitation Dynamics in Large Populations," Scholarly Articles 3196338, Harvard University Department of Economics.
    11. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
    12. 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.
    13. Nowak, Martin & Sasaki, Akira & Fudenberg, Drew & Taylor, Christine, 2004. "Emergence of Cooperation and Evolutionary Stability in Finite Populations," Scholarly Articles 3196331, Harvard University Department of Economics.
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