Communication Effort in Teams and in Games

Abstract

Quick and cheap communication networks may strengthen the case for the dispersal of organizations from one central site to many local ones. The case may be weakened if the dispersed persons behaved like members of a team before the dispersal but become self- interested players of a game after dispersal. To obtain some insight into these matters, the paper explores one very simple class of models. Each of N persons observes a signal that partly identifies the “week’s” (finite) game and then sends a chosen action (strategy) to a Center. Following the receipt of all N chosen actions, the Center puts them into force. Each person’s net payoff for the weak is the gross payoff determined for the week’s game minus a communication cost. Personi’s cost depends on the probabilities with which i sends alternative messages to the Center. We use the “information content” measure of classic Information Theory, multiplied by θ, the time required to transmit one bit. We study the “rule game” in which i chooses a rule that assigns a probability mixture over actions to each of i’s signals; in that gamei’s payoff is z’s average weekly gross payoff minus i’s communication cost. We find that (i) if an equilibrium N-tuple of rules exists, then it has to be an N- tuple in which true mixtures are not used; (ii) the existence of an equilibrium N-tuple is not guaranteed and the usual appeal to mixing over the possible N-tuples does not help, since such mixing has no meaning in our setting; (iii) even under the strong assumption that the gross payoff is identical for every person, there may be equilibria in which the dispersed persons communicate “too little” (from the team point of view) as well as equilibria in which they communicate “too much”; (iv) for very small θ and very large θ, equilibria exist in the identical-gross-payoff case. A great deal remains to be learned.