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Backward Induction and Model Deterioration

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Abstract

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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  • Francesco Squintani, 2001. "Backward Induction and Model Deterioration," RCER Working Papers 484, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:484
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    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; Information and Knowledge; Communication; Belief; Unawareness

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