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Deterministic approximation of best-response dynamics for the Matching Pennies game

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  • Gorodeisky, Ziv

Abstract

We consider stochastic dynamics for the Matching Pennies game, which behave, in expectation, like the best-response dynamics (i.e., the continuous fictitious play). Since the corresponding vector field is not continuous, we cannot apply the deterministic approximation results of Benaïm and Weibull [M. Benaïm, W. Weibull. 2003. Deterministic approximation of stochastic evolution in games. Econometrica 71, 873-903]. Nevertheless, we prove such results for our dynamics by developing the notion of a "leading coordinate."

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  • Gorodeisky, Ziv, 2009. "Deterministic approximation of best-response dynamics for the Matching Pennies game," Games and Economic Behavior, Elsevier, vol. 66(1), pages 191-201, May.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:1:p:191-201
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    References listed on IDEAS

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Ziv Gorodeisky, 2005. "Stability of Mixed Equilibria," Discussion Paper Series dp397, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    4. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 527-538.
    5. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    6. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 923-933, October.
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