Rationality and Common Knowledge

Interactive epistemology is the study of the distribution of knowledge among rational agents, usingmodal logic in the tradition of Hintikka (1962) and Kripke (1963), and agent rationality based on the rational actor model of economic theory, in the tradition of Von Neumann and Morgenstern (1944) and Savage (1954). Epistemic game theory, which is interactive epistemology adjoined to classical game theory (Aumann, 1987, 1995), has demonstrated an intimate relationship between rationality and correlated equilibrium (Aumann 1987, Brandenburger and Dekel 1987), and has permitted the rigorous specification of the conditions under which rational agents will play a Nash equilibrium (Aumann and Brandenburger 1995). A central finding in this research is that rational agents use the strategies suggested by game-theoretic equilibrium concepts when there is a communality of knowledge in the form of common probability distributions over the stochastic variables that arise in the play of the game (so-called common priors), and common knowledge of key aspects of the strategic interaction. We say an event E is common knowledge for agents i D 1; : : : ; n if the each agent i knows E, each i knows that each agent j knowsE, each agent k knows that each j knows that each i knows E, and so on (Lewis 1969, Aumann 1976). Specifying when individuals share knowledge and when they know that they share knowledge is among the most challenging of epistemological issues. Contemporary psychological research has shown that these issues cannot be resolved by analyzing the general features of high-level cognitive functioning alone, but in fact concern the particular organization of the human brain. Humans have a theory