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Convergence of best response dynamics in extensive-form games

Author

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  • Xu, Zibo

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

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.

Suggested Citation

  • Xu, Zibo, 2013. "Convergence of best response dynamics in extensive-form games," SSE/EFI Working Paper Series in Economics and Finance 745, Stockholm School of Economics, revised 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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    References listed on IDEAS

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    1. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    2. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
    3. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    4. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, January.
    5. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    6. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
    7. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    8. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
    9. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
    10. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
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    More about this item

    Keywords

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

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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