A Walrasian approach to bargaining games

Abstract

The paper presents and discusses an alternative approach to bargaining games. N-person bargaining games with complete information are shown to induce in a canonical way an Arrow-Debreu economy with production and private ownership. The unique Walras stable competitive equilibrium of this economy is shown to coincide with an asymmetric Nash bargaining solution of the underlying game with weights corresponding to the shares in production. In the case of an economy with equal shares in production, the unique competitive equilibrium coincides with the symmetric Nash bargaining solution. As this in turn represents the unique Shapley nontransferable utility (NTU) value our paper solves a problem posed by Shubik, namely to find a model in which the Shapley NTU value is a Walrasian equilibrium. “There has been some controversy about the interpretation of the λ-transfer-value … no consensus has yet emerged on the significance of these concerns, which had been addressed… in numerous explorations of the λ-transfer-value as a tool for analysing games and markets … ” (Roth, 1985).