The effect of the topology on the spatial ultimatum game

TL;DR

This paper investigates how different network topologies influence the evolution of strategies in a spatial ultimatum game, revealing that spatial structure significantly impacts outcomes, especially in disordered networks with small neighborhoods.

Contribution

It provides a detailed analysis of the impact of various network topologies on the spatial ultimatum game, highlighting the importance of spatial structure over neighborhood size.

Findings

Spatial topology significantly affects strategy evolution.

Disordered networks with small neighborhoods differ from fully connected networks.

Spatial structure influences game outcomes more than neighborhood size.

Abstract

In this work we present an analysis of a spatially non homogeneous ultimatum game. By considering different underlying topologies as substrates on top of which the game takes place we obtain nontrivial behaviors for the evolution of the strategies of the players. We analyze separately the effect of the size of the neighborhood and the spatial structure. Whereas this last effect is the most significant one, we show that even for disordered networks and provided the neighborhood of each site is small, the results can be significantly different from those obtained in the case of fully connected networks.