Evolution of fairness in the one-shot anonymous Ultimatum Game

Abstract

Classical economic models assume that people are fully rational and selfish, while experiments often point to different conclusions. A canonical example is the Ultimatum Game: one player proposes a division of a sum of money between herself and a second player, who either accepts or rejects. Based on rational self-interest, responders should accept any nonzero offer and proposers should offer the smallest possible amount. Traditional, deterministic models of evolutionary game theory agree: in the one-shot anonymous Ultimatum Game, natural selection favors low offers and demands. Experiments instead show a preference for fairness: often responders reject low offers and proposers make higher offers than needed to avoid rejection. Here we show that using stochastic evolutionary game theory, where agents make mistakes when judging the payoffs and strategies of others, natural selection favors fairness. Across a range of parameters, the average strategy matches the observed behavior: proposers offer between 30% and 50%, and responders demand between 25% and 40%. Rejecting low offers increases relative payoff in pairwise competition between two strategies and is favored when selection is sufficiently weak. Offering more than you demand increases payoff when many strategies are present simultaneously and is favored when mutation is sufficiently high. We also perform a behavioral experiment and find empirical support for these theoretical findings: uncertainty about the success of others is associated with higher demands and offers; and inconsistency in the behavior of others is associated with higher offers but not predictive of demands. In an uncertain world, fairness finishes first.cooperation | prosociality | stochastic dynamics

The role of self-interest in elite bargaining

“…This empirical result supports theoretical models that show demands for higher offers can persist in a population where agents engage in social learning (14,15). In fact, these models suggest that experience can cause both offers and demands to approach a 50/50 split (14).…”

“…This may help to explain why policy elites, such as the diplomats who negotiate treaties on topics like global warming, pay close attention to distributional concerns even though such concerns have been a perennial source of policy gridlock. (14,15). Therefore, it is plausible that higher levels of learning and experience in elite populations could push them further from the predictions made by standard models, suggesting that the tendency to reject low offers (found in many Western populations) could persist in populations of elite bargainers.…”

“…Theoretical models in evolutionary game theory suggest that learning can cause demands to rise over time because proposers with less experience are initially uncertain about the distribution of plausible demands, leading them to make higher offers that are closer to a 50/50 split (14,15). By making higher offers, proposers improve the payoff of responders who make higher demands, and this increases the chance that high-demand strategies are copied (14,15). A selection process could also achieve the same outcome as a learning process if less successful bargainers are weeded out over time.…”

“…Although some models have focused on prosocial motives, such as a preference for "fairness" or an aversion to inequity (8,9), other work has found no link between rejections in the ultimatum game and prosocial behavior in other games (10). This suggests that humans' tendency to reject low offers in the ultimatum game may stem from other sources, such as spite (11,12), culture (3,13), and generalized forms of social learning (14,15).…”

Economic Rationality in the Ultimatum Game

“…Mezidruhová a vnitrodruhová interakce v rámci evoluce je předmětem studia četných modelů a protichůdných teorií. Některé práce v evoluční teorii her dokumentují, že přírodní výběr upřednostňuje férovost [Rand et al, 2013]. Některé dokonce tvrdí, že jedinci charakterizovaní jako féroví a vlídní mají evoluční výhodu [Wang, 2015].…”