Expected Utility Preferences versus Prospect Theory Preferences in Bargaining

Are individuals always better off when their preferences can be represented by expected utility? I study this question in a bargaining game where individuals bargain over a pie of fixed size, and I contrast the share received in the long-run by expected utility maximisers with the share they would receive if their preferences were described by prospect theory preferences instead when, in either case, they bargain with expected utility maximisers. I present a necessary and sufficient condition for individuals to obtain a higher share of the pie if their preferences obey prospect theory rather than expected utility. I decompose the effect that the three features that characterise prospect theory preferences -- reference point dependence, loss-aversion and probability weighting -- have on the bargaining outcome, and show that loss-aversion does not have any effect on the outcome of the bargaining process, reference-point dependent preference confers an unambiguous advantage and probability weighting is unambiguously disadvantageous. This ties in with the main result outlined earlier: if the upward pull of reference point dependence is relatively stronger than the downward push of probability weighting, then individuals are better off with prospect theory preferences than with expected utility preferences, and vice-versa.