Thoron, Sylvie: Strategic Reactions of a Frustrated Coalition
World Conference Econometric Society, 2000, Seattle

Sylvie Thoron, GREQAM
Strategic Reactions of a Frustrated Coalition
Session: C-13-3  Wednesday 16 August 2000  by Thoron, Sylvie
I analyse three non cooperative models of coalition formation. Each model has two steps. In the first step, each player has to choose the coalition to which she wishes to belong. The issue is a coalition structure. In the second step, a game between the coalitions of the structure determines the payments. But the models differ in the way they treat the reaction of a coalition which loses one or more of its members (a "frustrated coalition"). In the first model (Von Neumann and Morgenstern [1944]), this frustrated coalition is assumed to "fall apart". In the second model (Hart and Kurz [1983]), the remaining members of the coalition stay together. I propose a third game in which the frustrated coalition consider each of the possible reactions as a strategy. The reaction is then treated as a best reply. Which coalition structures turn out to be stable will depend on the model of coalition formation, that is, on the conjectures, and on the final game between coalitions which will determine the payoffs. To represent the final game, I propose a Cobb Douglass payment function in which the two arguments are the size of the coalition and the number of competitors. There are positive externalities between coalitions in a given structure. This payment function is quite general and very different examples such as the Owen value in a bargaining game and the Cournot solution for an oligopoly turn out to be special cases. For a large class of pay-off functions, including the Cournot case, the grand coalition is stable in the G-model whereas the structure in which all the players are independent is the only stable structure in the D-model. In the third model, the stable structures are intermediate and contain several coalitions which may be of different sizes.

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