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

¹ Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences - P.O. Box 49, H-1525 Budapest, Hungary, EU
² Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia, EU

Received: 17 July 2012
Accepted: 4 October 2012

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.