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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 745:
Convergence of best response dynamics in extensive-form games

Zibo Xu ()

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.

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

JEL-Codes: C73; D83; (follow links to similar papers)

44 pages, June 24, 2013, Revised June 28, 2013

The author would like to acknowledge financial support from the Knut and Alice Wallenberg Foundation.

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