Aumann (1976) put forward a formal definition of common knowledge and used it to prove that two "like minded" individuals cannot "agree to disagree" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes' rule) on the basis of private...

We provide an introduction to interactive belief systems from a qualitative and semantic point of view. Properties of belief hierarchies are formulated locally. Among the properties considered are "Common belief in no error" (which has been shown to have important game theoretic applications),...

We consider interactive epistemic models where individuals are described by both their "knowledge" and their "beliefs." Three intersubjective consistency conditions are examined: Intersubjective Caution (if an individual believes something to be common belief then he knows it to be common...

From the point of view of Nash implementation theory, the result yields a partial characterization of the restrictions entailed by Nash implementability. Alternatively, the result can be viewed as a possibility theorem on the dominant-strategy-implementability of monotone SCCs via set-valued...

We give an introduction to the literature on the epistemic foundations of solution concepts in game theory. Only normal-form games are considered. The solution concepts analyzed are rationalizability, strong rationalizability, correlated equilibrium and Nash equilibrium. The analysis is carried...

The "Harsanyi Doctrine" asserts that differences in individuals' beliefs are to be attributed entirely to differences in information. In its embodiment as a Common Prior assumption it is central to the economics of information and the foundations of game theory. This paper attempts to provide a...

Condorcet domains are sets of preference orders such that the majority relation corresponding to any profile of preferences from the domain is acyclic. The best known examples in economics are the single-peaked, the single-crossing, and the group separable domains. We survey the latest...