Accuracy in strategy imitations promotes the evolution of fairness in the spatial ultimatum game

TL;DR

This paper demonstrates that spatial structure and the accuracy of strategy imitation significantly influence the evolution of fairness in the spatial ultimatum game, with finer strategy choices promoting fairer outcomes.

Contribution

It shows that spatiality promotes fairness only with sufficiently fine-grained strategies and that high imitation accuracy leads to the fairest outcomes in the evolutionary process.

Findings

Finer strategy sets promote coexistence of rational strategies.

Larger strategy sets tend to favor dominant but less fair strategies.

Highest fairness is achieved with the most accurate strategy imitation.

Abstract

Spatial structure has a profound effect on the outcome of evolutionary games. In the ultimatum game, it leads to the dominance of much fairer players than those predicted to evolve in well-mixed settings. Here we show that spatiality leads to fair ultimatums only if the intervals from which the players are able to choose how much to offer and how little to accept are sufficiently fine-grained. Small sets of discrete strategies lead to the stable coexistence of the two most rational strategies in the set, while larger sets lead to the dominance of a single yet not necessarily the fairest strategy. The fairest outcome is obtained for the most accurate strategy imitation, that is in the limit of a continuous strategy set. Having a multitude of choices is thus crucial for the evolution of fairness, but not necessary for the evolution of empathy.