Overcoming unfairness via repeated interactions in mini-ultimatum game

2026-04-04

AI Summary

This study investigates how repeated interactions foster the evolution of fairness, focusing on the resilience of fair strategies against unfair mutants in the mini-ultimatum game. By constructing a repeated-game framework within a two-type population, it uniquely integrates reactive strategies with evolutionary stability theory and introduces a non-local mutation dynamics model suitable for finite populations. The analysis reveals a critical effective interaction length that sustains fairness: short-term fairness relies on reciprocity-based compliant strategies, whereas long-term fairness is jointly maintained by compliant proposers and fair responders. Moreover, certain reactive strategies are shown to effectively promote and stabilize fair outcomes.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study addresses a gap in the literature by theoretically modelling the evolution of fairness within a repeated mini-ultimatum game. Specifically, we construct a repeated-game framework where offerers and accepters interact using reactive strategies. We then investigate whether fair reactive strategy pairs are resilient against unfair mutants in a two-species population. By analyzing short-term evolutionary stability via the concept of two-species evolutionary stable strategy, we identify a critical effective game length: below this value, fairness is promoted by offerers and accepters who comply with their partner's past actions. Above this critical value, fairness is maintained by `complier' offerers and fair accepters. We also show that specific reactive strategies effectively facilitate the emergence and sustenance of fairness in long-term mutation-selection dynamics. To this end, we develop a two-population stochastic dynamics model -- a generalization of classical adaptive dynamics -- that accounts for finite population sizes and non-local mutants in the reactive strategy space.

Problem

• fairness
• repeated interactions
• mini-ultimatum game
• evolutionary stability
• reactive strategies

Innovation

• repeated mini-ultimatum game
• reactive strategies
• two-species evolutionary stable strategy
• stochastic dynamics
• fairness evolution