Synchronic information, knowledge and common knowledge in extensive games

Research in Economics 53 (1):77-99 (1999)
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Abstract

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern 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

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Giacomo Bonanno
University of California, Davis

Citations of this work

A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Cham, Switzerland: Springer International Publishing. pp. 289-337.
Johan van Benthem on Logic and Information Dynamics.Alexandru Baltag & Sonja Smets (eds.) - 2014 - Cham, Switzerland: Springer International Publishing.
On the use (and abuse) of Logic in Game Theory.Eric Pacuit - 2015 - Journal of Philosophical Logic 44 (6):741-753.
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References found in this work

Reasoning About Knowledge: An Overview.Joseph Y. Halpern - 1988 - Journal of Symbolic Logic 53 (2):660-661.
La connaissance commune en logique modale.Luc Lismont - 1993 - Mathematical Logic Quarterly 39 (1):115-130.
On the Logic of Common Belief.Giacomo Bonanno - 1996 - Mathematical Logic Quarterly 42 (1):305-311.

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