Bilateral bargaining in networks

Each connected pair of nodes in a network can jointly produce one unit of surplus. A maximum number of linked nodes is selected in every period to bargain bilaterally over the division of the surplus, according to the protocol proposed by Rubinstein and Wollinsky [Equilibrium in a market with sequential bargaining, Econometrica 53 (1985) 1133–1150]. All pairs, which reach an agreement, obtain the (discounted) payoffs and are removed from the network. This bargaining game has a unique subgame perfect equilibrium that induces the Dulmage–Mendelsohn decomposition (partition) of the bipartite network (of the set of nodes in this network).