Bargaining and efficiency in networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain.