Coalition Formation in a Contest Game with Three Heterogeneous Players

We analyze the incentive for cooperation of three players differing in their efficiency of effort in a contest game. We concentrate on the non-cooperative bargaining foundation of a coalition formation, and therefore, we adopt a two-stage model. In the first stage, individuals form coalitions following a bargaining protocol similar to the one proposed by Gul. Afterwards, coalitions play the contest game of Esteban and Ray within the resulting coalition structure of the first stage. We find that the grand coalition forms whenever the distribution of the bargaining power in the coalition formation game is equal to the distribution of the relative efficiency of effort. Finally, we use the case of equal bargaining power for all individuals to show that other types of coalition structures may be observed as well.