Learning with perfect information |
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Authors: | Pradeep Dubey Ori Haimanko |
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Institution: | a Center for Game Theory, Department of Economics, SUNY at, Stony Brook, NY 11794, USA;b Department of Economics, Ben-Gurion University, Beer Sheva 84105, Israel |
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Abstract: | For extensive form games with perfect information, consider a learning process in which, at any iteration, each player unilaterally deviates to a best response to his current conjectures of others' strategies; and then updates his conjectures in accordance with the induced play of the game. We show that, for generic payoffs, the outcome of the game becomes stationary, and is consistent with Nash equilibrium. In general, if payoffs have ties or if players observe more of each others' strategies than is revealed by plays of the game, the same result holds provided a rationality constraint is imposed on unilateral deviations: no player changes his moves in subgames that he deems unreachable, unless he stands to improve his payoff there. Moreover, with this constraint, the sequence of strategies and conjectures also becomes stationary, and yields a self-confirming equilibrium. |
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Keywords: | Learning in extensive form games Perfect information Self-confirming and Nash equilibria Objective updates Convergence in finite time |
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