Imitation of Success Leads to Cost of Living Mediated Fairness in the Ultimatum Game

TL;DR

This paper presents a social imitation model incorporating energy, cost of living, and reproduction, explaining the emergence of fairness and non-Nash strategies in the Ultimatum game across diverse societies.

Contribution

It introduces a novel imitation-based model that links internal energy dynamics with social fairness behaviors in the Ultimatum game, supported by empirical data analysis.

Findings

Imitation leads to correlation between selfishness and cost of living.

Non-Nash sharing strategies naturally emerge in stable societies.

Model captures qualitative aspects of human behavior in diverse cultures.

Abstract

The mechanism behind the emergence of cooperation in both biological and social systems is currently not understood. In particular, human behavior in the Ultimatum game is almost always irrational, preferring mutualistic sharing strategies, while chimpanzees act rationally and selfishly. However, human behavior varies with geographic and cultural differences leading to distinct behaviors. In this paper, we analyze a social imitation model that incorporates internal energy caches (e.g., food/money savings), cost of living, death, and reproduction. We show that when imitation (and death) occurs, a natural correlation between selfishness and cost of living emerges. However, in all societies that do not collapse, non-Nash sharing strategies emerge as the de facto result of imitation. We explain these results by constructing a mean-field approximation of the internal energy cache informed by time-varying distributions extracted from experimental data. Results from a meta-analysis on geographically diverse ultimatum game studies in humans, show the proposed model captures some of the qualitative aspects of the real-world data and suggests further experimentation.