Multilateral bargaining in networks: On the prevalence of inefficiencies

We introduce a noncooperative multilateral bargaining model for network-restricted environments. In each period, a randomly selected proposer makes an offer by choosing 1) a coalition, or bargaining partners, among the neighbors in a given network and 2) monetary transfers to each member in the coalition. If all the members in the coalition accept the offer, then the proposer buys out their network connections and controls the coalition thereafter. Otherwise, the offer dissolves. The game repeats until the grand-coalition forms, after which the player who controls the grand-coalition wins the unit surplus. All the players have a common discount factor.

The main theorem characterizes a condition on network structures for efficient equilibria. If the underlying network is either complete or circular, an efficient stationary subgame perfect equilibrium exists for all discount factors: all the players always try to reach an agreement as soon as practicable and hence no strategic delay occurs. In any other network, however, an efficient equilibrium is impossible if a discount factor is greater than a certain threshold, as some players strategically delay an agreement. We also provide an example of a Braess-like paradox, in which the more links are available, the less links are actually used. Thus, network improvements may decrease social welfare.

This paper, at least in two reasons, concentrates on unanimity-game situations in which only a grand-coalition generates a surplus. First, analyzing unanimity games is enough to show the prevalence of inefficiencies. If any of proper subcoalitions generates a partial surplus, an efficient equilibrium is impossible even in complete networks for high discount factors, as a companion paper1 shows. Second, in unanimity games we can investigate the role of network structure on strategic delay controlling network-irrelevant factors.