Modeling Bargaining Competition: Nash-in-Shapley vs. Nash-in-Nash

Abstract

In this paper, we document two shortcomings of Nash-in-Nash bargaining: outcomes depend on who earns operating profit (a violation of the Coase Theorem); and "schizophrenia," parties behaving "as if" they were bargaining against themselves. Schizophrenia makes makes the pre-merger equilibrium more competitive, and mergers more anti-competitive, than the "Nash-in-Shapley" alternative in which firms bargain in recognition of how their bargains affect final imputations. We find that even when parties bargain bilaterally and independently, they reach cooperative outcomes if they are linked by a chain of bilateral agreements.

Keywords: Bargaining, Contingent Contracts, Nash-in-Shapley, Nash-in-Nash, Vertical and Horizontal Mergers

JEL Classification: C78, D86, L14, L41, L42, G34