SSE/EFI Working Paper Series in Economics and Finance
Convergence of best response dynamics in extensive-form games
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
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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