The electronic mail game: Strategic behavior under “almost common knowledge”

This paper addresses a paradoxical game theoretic example which is closely related to the coordinated attack problem and shows that even if a large (but finite) number of propositions of the type "i knows that j knows that i knows... that the game is G" are true, the game theory situation is very different from when the coordination game played is common knowledge.

Abstract

A very basic assumption in all studies of game theory is that the game is "common knowledge." Following John Harsanyi (1967), situations without common knowledge are analyzed by a game with incomplete information. A player's information is characterized by his "type." Each player "knows" his own type and the prior distribution of the types is common knowledge. Jean-Francois Mertens and Samuel Zamir (1985) have shown that under quite general conditions one can find type spaces large enough to carry out Harsanyi's program and to transform a situation without common knowledge into a game with incomplete information in which the different types may have different states of knowledge. Harsanyi's method became the cornerstone of all modern analyses of strategic economic behavior in situations with asymmetric information (i.e., most of the theoretical Industrial Organization literature).