The purpose of this paper is to study the effect of a change in an individual's degree of risk aversion on the perfect Bayesian Nash equilibrium in a simple model of bargaining. I find that, contrary to the results in the axiomatic model with riskless outcomes due to Nash, an opponent may be made worse off by such a change. Further, an individual may want to take an action that identifies him as more, rather than less, risk averse than he really is. In the course of the analysis, I fully characterize the equilibria of a class of “wars of attrition” with incomplete information, and single out one as “perfect” in a certain sense; this result may be of independent interest.

Introduction

The role of risk aversion in bargaining has been widely studied within the axiomatic framework of Nash (1950) (see, for example, Roth (1979), Perles and Maschler (1981)). It has been found that if the negotiation concerns riskless outcomes, then the more risk averse an individual is, the higher the payoff of his opponent. Related results show that in this case it is to the advantage of an individual to “pretend” to be less risk averse than he really is (Kurz (1977, 1980), Thomson (1979), Sobel (1981)). These results have some intuitive appeal: Given any (probabilistic) beliefs about the behavior of his opponent, it seems that an individual should behave more cautiously, the more risk averse he is.