We characterize the max min of repeated zero-sum games in which player one plays in pure strategies conditional on the private observation of a fixed sequence of random variables. Meanwhile we introduce a definition of a strategic distance between probability measures, and relate it to the standard Kullback distance.

We consider the “and” communication device that receives input from two players and outputs the public signal yes if both inputs are yes and outputs no otherwise. We prove that no correlation can securely be implemented through this device, even if an infinite number of communication rounds are allowed.

We introduce the notion of an information structure I as being richer than another J when for every game G, all correlated equilibrium distributions of G induced by J are also induced by I. In particular, if I is richer than J then I can make all agents as well off as J in any game. We also define J to be faithfully reproducible from I when all the players can compute from their information in I “new information” that reproduces what they could have received from J. Our main result is that I is richer than J if and only if J is faithfully reproducible from I.

Correlated equilibria and communication equilibria are useful notions to understand the strategic effects of information and communication. Between these two models, a protocol generates information through communication. We define a secure protocol
as a protocol from which no individual may have strategic incentives to deviate and characterize these protocols.

Lorsque des possibilités de communication existent, un protocole désigne un ensemble de règles utilisées par les agents pour échanger de l’information. Nous définissons un protocole robuste comme un protocole duquel aucun agent n’a intérêt à dévier, et caractérisons ces protocoles.

This paper proves a Folk Theorem for overlapping generations games in the case where the mixed strategies used by a player are not observable by the others, but only their realizations are public.