One-to-many bargaining with indissoluble agreements

Montez, JP (2012) One-to-many bargaining with indissoluble agreements. Working Paper. London Business School.

Abstract

We study a model where a central player (the principal) bargains bilaterally with each of several players (the agents) to create and share the surplus of a coalitional game. It is known that if the payments agreed with the agents are rebargained in case any bilateral negotiation breaks down, then the Shapley value is the unique e¢ cient and individual rational outcome consistent with bilateral Nash bargaining. Here we show that when the agreed payments cannot be rebargained, i.e., they are indissoluble, that outcome is also unique but coincides instead with the Nucleolus of an associated bankruptcy problem. We provide a strategic foundation for this outcome. Then we study how the ability to rebargain affects the principals' payoff according to the properties of the surplus function. We find, for example, that indissoluble agreements hurt the principal when agents are complements and they benefit him when they are substitutes.