Communication Games

Abstract

In the analysis of n-person games with side payments it is often assumed that all players will cooperate with each other and therefore the formation of the grand coalition is taken for granted. This of course is not the case in many practical situations where only partial cooperation may be sought by some of the players. In several circumstances this may be due to a lack of communication among several participants. These situations were first considered by Myerson (1977) who studied in particular the problem of how the reward (or the cost) resulting from the corresponding games should depend on which players cooperate with each other. As far as this article is concerned, the method of research has been to impose various communication graphs on groups of players in order to describe both the communication properties and the economic possibilities. By borrowing from the theory of cooperative games with coalitional structures as established by Aumann and Drèze (1974), a unique allocation rule which is both efficient and fair can be derived and shown to be essentially given by the Shapley value of a restricted game. Furthermore, it turns out that if the game is superadditive, then the proposed allocation rule is stable, that is to say two players can always benefit from reaching bilateral agreements.