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Convergence of best response dynamics in extensive-form games

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  • Xu, Zibo

    ()
    (Dept. of Economic Statistics, Stockholm School of Economics)

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    Abstract

    We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In a perfect-information game where each player can only move at one node, we prove that all interior approximate best response dynamics converge to the backward induction equilibrium, which is hence the socially stable strategy in the game.

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    File URL: http://swopec.hhs.se/hastef/papers/hastef0745.pdf
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    Bibliographic Info

    Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 745.

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    Length: 44 pages
    Date of creation: 24 Jun 2013
    Date of revision: 28 Jun 2013
    Handle: RePEc:hhs:hastef:0745

    Note: The author would like to acknowledge financial support from the Knut and Alice Wallenberg Foundation.
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    Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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    Related research

    Keywords: Convergence to Nash equilibrium; games in extensive form; games of perfect information; Nash equilibrium components; best response dynamics; fictitious play; socially stable strategy.;

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    1. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp309, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Apr 2003.
    2. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, Econometric Society, vol. 63(6), pages 1371-99, November.
    3. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information, EconWPA 9905002, EconWPA, revised 23 Mar 2000.
    4. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, Elsevier, vol. 83(2), pages 260-285, December.
    5. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, American Economic Association, vol. 93(5), pages 1830-1836, December.
    6. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
    7. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262033054, December.
    8. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199247868, October.
    9. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
    10. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, Elsevier, vol. 65(2), pages 626-643, March.
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