A Model of Protocoalition Bargaining with Breakdown Probability

Abstract

This paper analyses a model of legislative bargaining in which parties form tentative coalitions (protocoalitions) before deciding on the allocation of a resource. Protocoalitions may fail to reach an agreement, in which case they may be dissolved (breakdown) and a new protocoalition may form. We show that agreement is immediate in equilibrium, and the proposer advantage disappears as the breakdown probability goes to zero. We then turn to the special case of apex games and explore the consequences of varying the probabilities that govern the selection of formateurs and proposers. Letting the breakdown probability go to zero, most of the probabilities considered lead to the same ex post pay-off division. Ex ante expected pay-offs may follow a counterintuitive pattern: as the bargaining power of weak players within a protocoalition increases, the weak players may expect a lower pay-off ex ante.

Coalition Formation in Games with Externalities

“…Recently there has been renewed interest in models where negotiations to form a coalition can break down, resulting in bargaining returning to the starting point (see[30,56]). These models have not been extended to partition function games.…”