Credible Nash Bargaining Solution for Bilateral Trading Networks

TL;DR

This paper introduces the credible bargaining solution for bilateral trading networks, refining stability by incorporating credible outside options, and provides theoretical properties and characterizations of this solution.

Contribution

It proposes a new solution concept that refines stability in bilateral markets by considering credible outside options, with existence proofs and characterizations.

Findings

The credible bargaining solution exists under general conditions.

Characterization of the solution in the unit-surplus case.

Identification of essential links in the network.

Abstract

We study surplus division in network constrained bilateral matching markets with transferable utility. We introduce a new solution concept, the credible bargaining solution, which refines stability by requiring that, for each matched pair of buyer and seller, surplus be divided according to the Nash bargaining solution with respect to credible outside options, defined as their payoffs in some stable outcome of the submarket obtained by removing their link. We establish general properties of the credible bargaining solution, prove existence, and provide a complete characterization in the unit-surplus case based on the notion of essential links.