Ecologies of Preferences with Envy as an Antidote to Risk-Aversion in Bargaining

Models have been put forward recently that seem to be successful in explaining apparently anomalous experimental results in the Ultimatum Game, where responders reject positive offers. While imparting fixed preference orders to fully rational agents, these models depart from traditional models by assuming preferences that take account not only of the material payoff to oneself, but also of that which is given to others. However, they leave open the question of how an agent’s economic survival is helped by a preference order that advises him to leave money on the table. Our answer is that, indeed, doing so does not help. But that the same envious preference order that ill advises in some circumstances to reject an “insultingly” small offer, advises well in other circumstances, when it helps the same agent to overcome his risk-aversion and to offer a risky, tough offer that yields him a higher expected dollar gain. We show the existence of population distributions where the two effects exactly balance out across different preference types. These distributions are asymptotically stable, stationary, and inefficient, in which different preferences are represented, and where, as commonly observed in an Ultimatum Game, positive offers are made, of which some are rejected with positive probability. Our theory yields new testable hypotheses.