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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. Xu, Zibo, 2013. "Stochastic stability in finite extensive-form games of perfect information," SSE/EFI Working Paper Series in Economics and Finance 743, Stockholm School of Economics.
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    Cited by:

    1. Stéphane Le Roux & Arno Pauly, 2020. "A Semi-Potential for Finite and Infinite Games in Extensive Form," Dynamic Games and Applications, Springer, vol. 10(1), pages 120-144, March.

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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.;
    All these keywords.

    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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