Suppose we replace ``knowledge'' by ``belief with probability p'' in standard de®nitions of common knowledge. Very di ̈erent notions arise depending on the exact de®nition of common knowledge used in the substitution. This paper demonstrates those di ̈erences and identi®es which notion is relevant in each of three contexts: equilibrium analysis in incomplete information games, best response dynam...

Note: This paper is a draft of a survey of common knowledge prepared for the Journal of Economic Perspectives. Another, more technical version, has been prepared for the Handbook of Game Theory. I wish to acknowledge many inspiring conversations, over the course of many years, I have had with Bob Aumann on the subject of common knowledge.

In this paper we introduce a new type of knowledge operator, called evidencebased knowledge, intended to capture the constructive core of common knowledge. An evidence-based knowledge system is obtained by augmenting a multi-agent logic of knowledge with a system of evidence assertions t :φ (“t is an evidence for φ”) based on the following plausible assumptions: 1) each axiom has evidence; 3) e...

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in Alberucci and Jäger [1], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.

The paper consists of two parts. The rst one is a concise introduction to epistemic (both propositional and predicate) logic with common knowl-ege operator. As the full common knowledge predicate logics are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at...

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 ga...

The name Generic Common Knowledge (GCK) was suggested by Artemov to capture a state of a multi-agent epistemic system that yields iterated knowledge I(φ): ‘any agent knows that any agent knows that any agent knows. . .φ’ for any number of iterations. The generic common knowledge of φ, GCK(φ), yields I(φ),

In an economy with a fixed exchange rate regime that suffers an adverse shock, we study the delay strategies of speculators that may trigger an endogenous devaluation before it occurs exogenously. The game played by the speculators has a unique symmetric Nash equilibrium which is a strongly rational expectation equilibrium. A higher uncertainty about the initial level of reserves of the Central...

The paper consists of two parts. The rst one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with...