A prospect theory Nash bargaining solution and its stochastic stability

We consider the long-run outcomes of bargaining games when players obey prospect theory. We extend the evolutionary bargaining model of Young (1993) to a two-stage Nash demand game. Two players simultaneously choose whether to exercise an outside option in the first stage and play the Nash demand game in the second stage, which will be reached only if neither player exercises the outside option. We address the influence on the stochastically stable division of reference-dependent preferences where the reference point is the value of the outside option. We show that the division consistently differs from the Nash bargaining solution under expected utility theory. Inspired by this, we propose a prospect theory Nash bargaining solution, which coincides with the stochastically stable division.