Market Organization: Noncooperative Models of Coalition Formation

Abstract

I apply three noncooperative models of coalition formation to a Cournot olygopoly. In each model, each firm has to choose the coalition it wants to belong to. But each of this models is characterised by a different assumption that defines what happens to a coalition from which one or more players depart (which we shall refer to as a “depleted coalition”). In the first model proposed by Von Neumann and Morgenstern [1944], this depleted coalition is assumed to “fall apart”, in the second one proposed by Hart and Kurz [1983], it is assumed to “stick together”. I prove that the results depend crucially on the game of coalition formation. In the first model, the grand coalition is stable, in the second model, the unique stable structure is the structure in which all the firms are independent. In fact, The assumption that characterises the game of coalition formation has to be considered as a threat, the credibility of which has to be analysed. That is why I propose a third game in which members of a depleted coalition choose the reaction to adopt. It turns out that the members of such a coalition stick together as long as they are sufficiently numerous. As a result, the set of stable structures in this model depends on the number of firms, n. When this number is small, the grand coalition is the unique stable structure. But when the number of firms increases, asymmetrical coalition structures appear. For great value of n, stable structures appear with several coalitions, that can be of different sizes. We notice that, in this game with symmetric firms as players, the result can be asymmetric.