Defense mechanisms of empathetic players in the spatial ultimatum game

TL;DR

This paper introduces a spatial ultimatum game with discrete strategies, revealing complex dynamics like traveling waves and cyclic dominance, which shed light on the evolution of fairness and empathy in human behavior.

Contribution

The study presents a novel spatial ultimatum game model with discrete strategies, uncovering rich dynamical behaviors such as traveling waves and cyclic dominance not seen in continuous strategy models.

Findings

Discovery of traveling waves and cyclic dominance in the game dynamics

Identification of mixed stationary states and phase transitions

Revelation of complex phase diagram with hidden dynamics

Abstract

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the evolution of fairness, thus far considered continuous strategies have precluded the observation of solutions that would be driven by pattern formation. Here we introduce a spatial ultimatum game with discrete strategies, and we show that this simple alteration opens the gate to fascinatingly rich dynamical behavior. Besides mixed stationary states, we report the occurrence of traveling waves and cyclic dominance, where one strategy in the cycle can be an alliance of two strategies. The highly webbed phase diagram, entailing continuous and discontinuous phase transitions, reveals hidden complexity in the pursuit of human fair play.