Repeated bargaining with reference dependent preferences

We consider a two-player bargaining model in which one or both players have reference-dependent preferences, but are otherwise perfectly rational. Our behavioural assumption is that players with reference-dependent preferences prefer impasse to consuming strictly less than their current reference points. Reference points adjust each period according to some exogenously specified law of motion. When reference points do not adjust following disagreement, we show that disagreement does not arise in equilibrium, but they do influence the division of the pie. In contrast, when reference points adjust downwards following disagreement, disagreements arise and players may try to manipulate the reference point of their opponent. When reference points adjust downwards following a rejection, for a particular Markov equilibrium, we show that the set of feasible allocations can be divided into agreement and disagreement regions. In particular, there are thresholds such that if one (or more) player's reference point is above the threshold, disagreement necessarily arises.