The Ultimatum Game in Complex Networks

TL;DR

This paper investigates how cooperative behavior emerges in complex networks through the ultimatum game, considering different agent types and update rules, revealing how fairness develops in various topologies.

Contribution

It introduces a model of the ultimatum game with diverse agent types and analyzes their behavior on complex networks using replicator and social penalty dynamics.

Findings

Fairness emerges differently depending on network topology and agent type.

Social Penalty dynamics promote more equitable outcomes than natural selection.

Network structure significantly influences cooperation levels.

Abstract

We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an ultimatum game in complex networks. Specifically, three types of players are considered: (a) empathetic, whose aspiration level and offer are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration level and offer are independent. We analyze the asymptotic behavior of pure populations on different topologies using two kinds of strategic update rules. Natural selection, which relies on replicator dynamics, and Social Penalty, inspired in the Bak-Sneppen dynamics, in which players are subjected to a social selection rule penalizing not only the less fitted individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies.