Bargaining for assembly

We study a multilateral bargaining problem, where the buyer intends to purchase a subset of available items, each owned by a seller. The subset purchased must satisfy a notion of contiguity, which is modeled using graphs. The graph theoretic approach allows us to study different degrees of complementarity and substitutability between items. It also allows us to examine how degrees of complementarity and substitutability affect the share of surplus obtained by the buyer in the equilibrium of the bargaining game. We characterize necessary and sufficient conditions on the graphs for the buyer to extract full surplus in subgame perfect equilibrium. When the conditions are not met, we provide upper bounds on the equilibrium surplus share of the buyer.