The Evolution of Fair Offers with Low Rejection Thresholds in the Ultimatum Game

Abstract

The ultimatum game (UG) is widely used in economic and anthropological research to investigate fairness by how one player proposes to divide a resource with a second player who can reject the offer. In these contexts, fairness is understood as offers that are more generous than predicted by the subgame perfect Nash equilibrium (SPNE). A surprising and robust result of UG experiments is that proposers offer much more than the SPNE. These results have spawned many models aimed at explaining why players do not conform to the SPNE by showing how Nash equilibrium strategies can evolve far from the SPNE. However, empirical data from UG experiments indicate that players do not use Nash equilibrium strategies, but rather make generous offers while rejecting only very low offers. To better understand why people behave this way, we developed an agent-based model to investigate how generous strategies could evolve in the UG. Using agents with generic biological properties, we found that fair offers can readily evolve in structured populations even while rejection thresholds remain relatively low. We explain the evolution of fairness as a problem of the efficient conversion of resources into the production of offspring at the level of the group.\n\nSignificance StatementHuman generosity is widespread and far exceeds that of other social animals. Generosity is often studied experimentally with the ultimatum game, in which a proposer offers a split and a responder can either accept it or cancel the whole deal. A surprising result of ultimatum game experiments is that players are much more generous than predicted while only rejecting very low offers. This has presented a theoretical puzzle, since mathematical models have generally relied on high rejection levels--just below offer levels--to maintain generosity. Using evolutionary simulations, we explain both generous offers and the rejection of only low offers as a solution to the problem of how groups can efficiently convert resources into the production of offspring.