A scheme of plain conversation is constructed, which is a universal mechanism for all noncooperative games with incomplete information with at least four players, in the following sense: every solution that can be achieved by means of an arbitrary communication mechanism is a correlated equilibrium payoff of the game extended by the scheme of plain conversation. By a property of the correlated equilibrium, a similar result holds also with the Nash equilibrium solution concept. The universal mechanism can be used without any loss of efficiency. Copyright 1990 by The Econometric Society.

We study (costless) information transmission from a job applicant to an employer who must decide whether to hire him and, if so, which position to give him. We construct equilibrium payoffs requiring at least two signaling steps, or even that no deadline be imposed on the (plain) conversation. The set of communication equilibrium payoffs (achieved with the help of a communication device) is larger than the set of equilibrium payoffs of the plain conversation game but coincides with the set of correlated equilibrium payoffs.

but any convex combination of pairs of optimal strategies such that p(2, 2) = 0 satisfies p(1, 1) > 2 (with the obvious notation p(i, j) for the induced probability of row i and column j). However, the following is easily checked. Let I and J be the sets of pure strategies of player 1 and player 2 respectively in a zero-sum game G with value v. Then p = [p(i, i)I(, J) IXJ is a correlated equilibrium distribution for G if and only if for every E J such that p(jo) > 0, the conditional probability of player 2 over player l's actions given jo' [p (iIjo)]I , is an optimal strategy for player 1, yielding exactly v against jo and similarly for [p(jlio)]jEj, io E , p(io) > 0. Hence as conjectured by R. Aumann, if a pure strategy pair occurs with positive probability in a correlated equilibrium, then it occurs with positive probability in a pair of optimal strategies. Also, if one of the players has a unique optimal strategy, then every correlated equilibrium distribution concentrates on a pair of optimal strategies.

The Nash equilibrium concept may be extended gradually when the rules of the game are interpreted in a wider and wider sense, so as to allow preplay or even intraplay communication. A well-known extension of the Nash equilibrium is Aumann's correlated equilibrium, which depends only on the normal form of the game. Two other solution concepts for multistage games are proposed here: the extensive form correlated equilibrium, where the players can observe private extraneous signals at every stage and the communication equilibrium, where the players are furthermore allowed to transmit inputs to an appropriate device at every stage. We show that the set of payoffs associated with each solution concept has a canonical representation (in the spirit of the revelation principle) and is a convex polyhedron. We also provide for each concept a super-canonical game such that the set of payoffs associated with the solution concept is precisely the set of Nash equilibrium payoffs of this game.

In a differential information economy with quasi–linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints: the associated ex ante core is generically nonempty. However, we exhibit a well–behaved exchange economy in which this core is empty, even if goods are allocated through random mechanisms.