Stable and Balanced Outcome of Bilateral Bargaining in Networks
59 Pages Posted: 30 Dec 2022
Date Written: December 30, 2022
Abstract
In this paper, we study the generalized Nash bargaining solution of bilateral bargaining in any given network, which is equivalent to the bilateral balanced outcome of a cooperative game with a network structure. We first establish that it is without loss of generality to focus on any maximum-weight matching when we discuss the existence of stable outcomes and the uniqueness of balanced outcomes. Then we characterize the exact network structure and characteristic function that ensure the existence of stable and balanced outcomes. Finally, we provide the necessary and sufficient condition for the uniqueness of balanced payoffs of a general network. We also show that any balanced outcome of a general weighted network consists of hierarchical balanced structures in which the outside options of agents in structures with lower slack values do not depend on the ones with higher slack values, but not vice versa. Our work combines and contributes to the literature on Nash bargaining, cooperative games, and network games.
Keywords: maximum-weight matching, bilateral bargaining, stable outcome, balanced outcome, networks
JEL Classification: C71, C78, D31, D85
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