The Effect of Decision Weights in Bargaining Problems

Bargaining problems are considered where the preferences of the bargainers deviate from expected utility but can be modelled according to rank dependent utility theory. Under rank dependent utility two factors influence the risk attitude of a decision maker: the utility function and the probability weighting function. Arising from the same definition of risk aversion, two forms of risk aversion can be distinguished: utility risk aversion and probabilistic risk aversion.The main finding is that these two forms of risk aversion can have surprisingly opposite consequences for bargaining solutions that exhibit a weak monotonicity property. In particular, in a large class of bargaining problems both increased utility risk aversion and decreased probabilistic risk aversion of the opponent are advantagous for a player. This is demonstrated for the Kalai-Smorodinsky bargaining solution. The Nash bargaining solution does not behave regularly in this respect.