Gradual Bargaining

Abstract:     
We propose a model of gradual bargaining in the spirit of the Nash axiomatic theory. In this model the underlying set of payoff opportunities expands continuously with time. Unlike Nash's solution that predicts a single agreement for each bargaining problem, our solution yields a continuous path of agreements--one for each point in time. It emerges from a simple and intuitive differential equation. We discuss the relationship between the gradual solution and various solution concepts of the standard Nash framework, and characterize it axiomatically with the essential axiom being "Invariance with Respect to Increasing Transformations". By using the richer framework of gradual bargaining, our axiomatization resolves a well known impossibility result by Shapley (1969), and it allows to construct an ordinal solution. Furthermore, our approach deals with some of the shortcomings of Nash's axiomatization. In particular, our axiomatic characterization does not use the controversial axiom of IIA and the sets of payoff opportunities are not restricted to be convex. In the spirit of the Nash Program we propose several non cooperative bargaining models that sustain our solution. Finally, we apply our model to discuss the allocation of physical (or monetary) assets when individuals' risk aversion changes over time.

working papers series