Synchronic Information, Knowledge and Common Knowledge in Extensive Games

Abstract

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern (1944) with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of "maximum information" we are able to provide an alternative characterization of the meet of the information partitions.