Asymmetric Bargaining

In this paper I explore asymmetric coalitional bargaining. Players are possibly different in preferences and in probability to place threats; the agreements emerge randomly during negotiations. As a result, players negotiate with different degree of enthusiasm. I compute a solution that I call random type value. The random type value is the Shapley value when players have the same ability to place threats, the agreements are equally likely, and, either players have the same (possibly non-linear) preferences, or players like “in the same way” different agreements. In a pure bargaining game the random type value coincides with the Nash bargaining solution when the threat points and the agreements are uniformly distributed. This suggests that the random type value is well suited to model a broad range of bargaining games in a rich way. I provide two applications: the first one, to political games, where players are distinguishable by their “ideological profiles”; the second one, to incomplete contracts, where, ex-ante, a player can integrate with a partner in order to acquire a bargaining advantage over future trading parties.