Convergence of best response dynamics in extensive-form games
AbstractWe 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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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 745.
Length: 44 pages
Date of creation: 24 Jun 2013
Date of revision: 28 Jun 2013
Note: The author would like to acknowledge financial support from the Knut and Alice Wallenberg Foundation.
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Convergence to Nash equilibrium; games in extensive form; games of perfect information; Nash equilibrium components; best response dynamics; fictitious play; socially stable strategy.;
Find related papers by 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, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-30 (All new papers)
- NEP-EVO-2013-06-30 (Evolutionary Economics)
- NEP-GTH-2013-06-30 (Game Theory)
- NEP-HPE-2013-06-30 (History & Philosophy of Economics)
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