Coalition Bargaining in Repeated Games

Abstract

We consider an intertemporal game-theoretic framework in which different coalitions interact repeatedly over time. Both the terms of trade and the endogenous cooperation structure arising in this setup are characterized, in a protocol-free manner, when just three natural conditions are satisfied:

(C1) A coalition is formed with positive probability if, and only if, the shares obtained in this case by its members weakly exceed their respective share expectations.

(C2) Each matched coalition distributes the entire surplus among its members.

(C3) Members of any coalition are treated symmetrically with respect to their share expectations when the surplus of this coalition is distributed.

Our analysis primarily focuses on the limit scenario where the game ends each date with a vanishing probability. We show that, in this case, the cooperation structure and the shares are unique and display a number of interesting properties. In an application to trade networks, we show that, in a complete network, a unique price arises and agents specialize in either buying or selling. In an incomplete network, on the other hand, transactions occur, generally, at multiple prices and some agents become arbitrageurs that buy and sell at different prices.

Keywords: repeated multi-coalitional games; coalition formation; network games

JEL Classification: C71, C78