Legislative Bargaining and Coalition Formation

The finite horizon version of a popular legislative bargaining model due to Baron and Ferejohn is investigated. With three or more rounds of bargaining a continuum of distributions are supportable as subgame perfect equilibria in Markov strategies. Allowing for history dependent strategies subgame perfect equilibria can be constructed where strictly positive shares are given to a larger group of people than necessary for a minimal winning coalition and, if players are sufficiently patient, any distribution where every agent get a strictly positive share can be supported as a subgame perfect equilibrium. In sharp contrast to these results I obtain a generic uniqueness result when allowing for differences in players' time preferences. However, the unique backwards induction equilibrium in the perturbed game is non-stationary. Hence, neither the original (symmetric) game or the perturbed game provides any guidance for equilibrium selection in the infinite game