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