Distributive justice of bargaining and risk sensitivity

Abstract

In this paper we will point out some possibilities and limitations of the discussion of distributive justice by bargaining in the classical bargaining models. We start by considering a kind of bargaining situation where two persons with different risk aversions have to distribute a given quantity of a certain good. Then we define a model in which two bargaining situations are compared. In both situations two persons divide a quantity of a certain good; in the second situation one of the persons, say person 2, is replaced by a more risk averse person. From a well-known theorem of Kihlstrom, Roth and Schmeidler it follows that in the Nash solution, the Kalai-Smorodinsky solution and the Maschler-Perles solution person 1 prefers the situation with the more risk averse opponent. In both classes of problems the judgement of distributive justice is impossible because of an informational poverty of the classical bargaining model. We propose to integrate changes in the economic situation of the persons into the model. Therefore, in a third step, we compare two distributive situations, where differences in the situations are implied by changes in the initial endowments of the persons. Under the assumption that each person has a decreasing local risk aversion, we show that every reallocation of the initial endowments is enlarged or at least preserved by risk sensitive bargaining solutions. This fact has some significance for the discussion of distributive justice in social decision making by bargaining.