This project proposes a theory of recurrent negotiation by a coalition of parties in a multilateral long-term relationship (a repeated-game setting), such as a group of countries forming an international agreement to reduce greenhouse-gas emissions. In a given period of time, the coalition negotiates to coordinate on a full description of behaviour for all future contingencies. Our theory posits that the coalition’s agreement serves to coordinate the play of all parties, both coalition members and outsiders. This is the source of the coalition’s power. Outsiders lack any way of coordinating other than to follow the plan that the coalition announces, subject to incentive constraints. The modelling exercise builds on a standard framework of multilateral relational contracting with transfers and the concept of contractual equilibrium (Miller and Watson 2013), which incorporates a full account of bargaining and the exercise of bargaining power in each discrete period of interaction.

Results are provided on the extent to which a governing coalition can influence the behaviour of outside parties, with implications for efficiency and coalition size. A central question is whether, in equilibrium, a coalition can induce outside parties to behave non-myopically, such as to abate at higher levels than myopic free-riders would choose. In a setting with limited renegotiation opportunities, the answer is affirmative. In contrast, if the coalition can renegotiate in every period, then the answer is negative and outsiders behave myopically across periods, just as renegotiation complicates punishments and rewards between coalition members. Arrangements by the coalition to induce limited cooperation by outsiders between instances of renegotiation are characterized, with implications for agreements in the international context. The model also produces results on the optimal allocation of bargaining power within a coalition and coalition formation, both relevant for the design of institutions that facilitate negotiation.