Date of this Version

2-19-2002

Document Type

Working Paper

Publication Details

Jeffrey J. Kline (2002) Extensive games with time structures

Acknowledgements:I thank Yukihiko Funaki for suggesting that time consistency must be difficult to discuss in a game without a clearly defined time structure. I thank Mamoru Kaneko for encouraging me to pursue time structures in extensive games.

School of Business Working Paper ; No. 1, Feb. 19, 2002

© Copyright Jeffrey J. Kline and the School of Business, Bond University

Abstract

We introduce personal time-structures and common time-structures to extensive games. These structures restrict the class of extensive games of Kuhn [8]. We show that if a player has perfect recall, then the game is personally time-structured for him. In the other direction, there are many personally time-structured games that do not satisfy perfect recall. The only known condition on memory that is required by a personally time-structured game is that no player is absent-minded. Common time-structures, on the other hand, are not related to the perfect recall condition at all. An extensive game may have perfect recall and yet no common time-structure, and conversly, a game may have a common time-structure, and no player has perfect recall. Common time-structures are used to extend backward induction results to games with imperfect recall.

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