Unlike formal games, most social applications are not accompanied by a complete list describing all relevant actions. As a result, the most difficult task faced by the players is often to formulate a model of the interaction. While it is known how players may learn to play in a game they know, the issue of how their model of the game evolves over time is largely unexplored. This paper presents and analyzes a social earning constrction that explicitely keeps track of the evolution of models held by players who are able to solve perfect-information extensive form games (according to their models), and whose models depend on past observation of play. We introduce the possibility of small-probability model deterioration and show that, even when concerning only opponents' unobserved actions, such deterioration may upset the complete-model backward-induction solution, and yield a Pareto-improving long-run distribution of play. We derive necessary and sufficient conditions for the robustness of backward-induction path with respect to model deterioration. These conditions can be interpreted with a forward-induction logic, and are shown to be less demanding than the requirements for asymptotic stability of the backward-induction path under standad evolutionary dynamics. In all games where it may upset the backward-induction path, model deterioration may induce long-run distributions of play that correspond to non subgame perfect Nash equilibria.
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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number
484.
Length: 57 pages Date of creation: Jul 2001 Date of revision: Handle: RePEc:roc:rocher:484
Contact details of provider: Postal: UNIVERSITY OF ROCHESTER, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, HARKNESS 231 ROCHESTER NEW YORK 14627 U.S.A.
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Find related papers by JEL classification: C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games 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
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