Strategic bargaining, surplus sharing problems and the nucleolus

Abstract

Suppose that n agents are trying to reach an agreement on how to split an estate over which they have claims. They do so through decentralized negotiations instead of appealing to an arbitrator. In this context, I study a consistency-based multilateral bargaining game that allows for ‘partial agreements’ and ‘bilateral negotiations’. The solution to these bilateral negotiations is influenced by the outside option of going to the ‘contested garment’ court (recommended in the Talmud for bilateral problems). When the surplus to share is negative (bankruptcy), if the proposer is the highest claimant, the unique subgame perfect equilibrium (SPE) outcome is the nucleolus. If it is someone else, multiplicity of SPE outcomes might arise. When the surplus is positive, the prenucleolus is always obtained as the unique SPE outcome of the game.