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Hypothetical Knowledge and Games with Perfect Information

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  • Dov Samet

Abstract

A standard model for a game with complete information consists of a state space with partitions, and a specification of the strategies played in each state. We show that such models are inadequate for explaining players' behavior. We propose instead extended models in which it is possible to express not only knowledge but also hypothetical knowledge, i.e., theories regarding subgames that are known not to be reached. In such models strategies are no longer primitives. Each state specifies behavior rather than strategies, and the latter are derived using hypothetical knowledge. In extended models common knowledge of rationality does not imply backward induction. We describe an intuitive condition that guarantees backward induction. Moreover, it is possible to express formally the idea that the theories that support the backward induction path assume some irrationality off path.

Suggested Citation

  • Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, University Library of Munich, Germany, revised 17 Aug 1994.
    • Handle: RePEc:wpa:wuwpga:9408001
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    References listed on IDEAS

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    1. Ben-Porath, E., 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Papers 14-92, Tel Aviv - the Sackler Institute of Economic Studies.
    2. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 33-44.
    3. Ben-Porath, Elchanan, 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Foerder Institute for Economic Research Working Papers 275567, Tel-Aviv University > Foerder Institute for Economic Research.
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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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