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 the Nash solution, and characterize it axiomatically by using essentially one property, which is Invariance with Respect to Increasing Transformations. We intetrpret this property as an incentive compatibility requirement. By using the richer framework of gradual bargaining, our aproach avoids some of the shortcomings of Nash`s axiomatization. In particular we do not need the controversial axiom of the ILA and the sets of payoff opportunities need not 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.

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