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Hypothetical Knowledge and Games with Perfect Information

Listed author(s):
  • Dov Samet

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.

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Paper provided by EconWPA in its series Game Theory and Information with number 9408001.

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Length: 23 pages
Date of creation: 08 Aug 1994
Date of revision: 17 Aug 1994
Handle: RePEc:wpa:wuwpga:9408001
Note: 23 pages, Plain TeX (a couple of truncated lines were corrected).
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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.
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