Stochastic ultimatum game: Spite-driven resource feedback fosters fairness

2026-07-16

AI Summary

This study addresses a critical gap in the literature by examining the interplay among resource dynamics, spiteful behavior, and fairness—particularly how fairness evolves under conditions of resource scarcity versus abundance. The authors propose a stochastic ultimatum game model incorporating renewable resource dynamics and, for the first time, integrate spite into a resource-feedback game framework. Using mutation–selection-driven two-species stochastic evolutionary dynamics, they demonstrate that fairness naturally prevails when resource growth rates are high. Conversely, under low growth rates, spite indirectly fosters fairness by initiating a feedback loop—“spite → resource recovery → fairness”—thereby facilitating the emergence of fair behavior. These findings uncover key conditions and mechanisms underlying the evolution of fairness in repeated interactions, moving beyond traditional paradigms focused solely on cooperation.

Abstract

Resource scarcity can fundamentally encourage antisocial behaviour, whereas resource abundance can promote fair behaviour. Experimental evidence indeed suggests that scarcity induces spiteful behaviour, while repeated interactions enhance fairness. However, existing studies of game--environment feedback systems are largely confined to the evolution of cooperation and they overlook the interplay between resources, spite, and fairness. To address this lacuna, we develop a stochastic ultimatum game framework in which an offerer and an accepter repeatedly interact to negotiate exploitation of a self-renewable resource under the ownership of the offerer. Successful agreements deplete the resource, whereas unsuccessful agreements inhibit exploitation and facilitate replenishment. The mutation--selection driven two-species stochastic evolutionary dynamics reveal that the emergence of spite and fairness strongly depends on the resource growth rate. Fairness predominantly prevails for resources with high growth rates. Intriguingly, low resource growth rates give rise to a resource feedback loop driven by spite: spiteful behaviour dominates in the depleted state, facilitating transition of the resource state to replete state which, in turn, promotes fairness through repeated interactions.

Problem

• stochastic ultimatum game
• spite
• fairness
• resource feedback
• evolutionary dynamics

Innovation

• stochastic ultimatum game
• spite-driven feedback
• resource dynamics
• fairness evolution
• evolutionary game theory