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Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory

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  • Michel Benaïm
  • Josef Hofbauer
  • Sylvain Sorin

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  • Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
    • Handle: RePEc:spr:dyngam:v:2:y:2012:i:2:p:195-205
    DOI: 10.1007/s13235-012-0040-0
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    References listed on IDEAS

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    1. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2006. "Stochastic Approximations and Differential Inclusions, Part II: Applications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 673-695, November.
    2. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    3. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    4. repec:dau:papers:123456789/1014 is not listed on IDEAS
    5. Chen, Hsiao-Chi & Friedman, James W. & Thisse, Jacques-Francois, 1997. "Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach," Games and Economic Behavior, Elsevier, vol. 18(1), pages 32-54, January.
    6. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    7. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    8. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    9. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    10. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    11. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    12. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    13. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    15. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
    16. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    17. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    18. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    19. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    20. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    21. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
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    Citations

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    Cited by:

    1. Arunselvan Ramaswamy & Shalabh Bhatnagar, 2017. "A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 648-661, August.
    2. Mansoor Saburov, 2022. "On Discrete-Time Replicator Equations with Nonlinear Payoff Functions," Dynamic Games and Applications, Springer, vol. 12(2), pages 643-661, June.
    3. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2020. "Best response algorithms in ratio-bounded games: convergence of affine relaxations to Nash equilibria," CSEF Working Papers 593, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Jos'e Pedro Gaiv~ao & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game," Papers 1912.06831, arXiv.org.
    5. José Pedro Gaivão & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the rock-paper-scissors game," Working Papers REM 2019/0108, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    6. José Pedro Gaivão & Telmo Peixe, 2021. "Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game," Dynamic Games and Applications, Springer, vol. 11(3), pages 491-511, September.
    7. Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
    8. Jason Milionis & Christos Papadimitriou & Georgios Piliouras & Kelly Spendlove, 2022. "Nash, Conley, and Computation: Impossibility and Incompleteness in Game Dynamics," Papers 2203.14129, arXiv.org.

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