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The time-preference Nash ...

## The time-preference Nash solution

Nir Dagan, Oscar Volij, and Eyal Winter

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### Abstract

We give an axiomatic characterization of the Time-Preference Nash Solution, a bargaining
solution that is applied when the underlying preferences are defined over streams of physical
outcomes. This bargaining solution is similar to the ordinal Nash solution introduced by
Rubinstein, Safra, and Thomson (1992), but it gives a different prediction when the set of
physical outcomes is a set of lotteries.

The primitives of a bargaining problem consist of a set, S, of feasible utility pairs and a disagree- ment point in it. The idea is that the set S is induced by an underlying set of physical outcomes which, for the purposes of the analysis, can be abstracted away. In a very influential paper Nash (1950) gives an axiomatic characterization of what is now the widely known Nash bargaining solution. Rubinstein, Safra, and Thomson (1992) (RST in the sequel) recast the bargaining problem into the underlying set of physical alternatives and give an axiomatization of what is known as the ordinal Nash bargaining solution. This solution has a very natural interpretation and has the interesting property that when risk preferences satisfy the expected utility axioms, it induces the standard Nash bargaining solution of the induced bargaining problem. This property justifies the proper name in the solution’s appellation. The purpose of this paper is to give an axiomatic characterization of the rule that assigns the time-preference Nash outcome to each bargaining problem.

Disscussion paper #265, Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem, Jerusalem (2001)

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### Cited by

- Oscar Volij and Eyal Winter,
**On risk aversion and bargaining outcomes,**
*Games and Economic Behavior* 41:120–140 (2002)
- Klaus Kultti and Hannu Vartiainen,
**Von Neumann-Morgenstern stable set bridges time-preferences to the Nash solution,**
*B.E. Journal of Theoretical Economics* 7(1), Contributions, Article 41 (2007)