Prejudice driven spite: A discontinuous phase transition in ultimatum game

2025-10-18

AI Summary

This study investigates how individual bias strength drives the emergence of resentment behavior in populations and its impact on social fairness and cooperation. Methodologically, we extend the ultimatum game by introducing a continuous bias parameter and develop a theoretical model integrating stochastic evolutionary dynamics with the replicator equation, incorporating both selection–replication and mutation–selection mechanisms. Our results reveal a first-order phase transition in resentment behavior as bias strength increases, characterized by a sharp, threshold-dependent onset; this transition becomes more pronounced and robust in the large-population limit. Beyond the critical threshold, resentment strategies become evolutionarily stable and persist indefinitely. This work provides the first game-theoretic characterization of a mutational mechanism through which bias triggers irrational retaliatory behavior, establishing a novel paradigm for understanding the social amplification of bias.

Technology Category

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

Application Category

• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

In a mix of prejudiced and unprejudiced individuals engaged in strategic interactions, the individual intensity of prejudice is expected to have effect on overall level of societal prejudice. High level of prejudice should lead to discrimination that may manifest as unfairness and, perhaps, even spite. In this paper, we investigate this idea in the classical paradigm of the ultimatum game which we theoretically modify to introduce prejudice at the level of players, terming its intensity as prejudicity. The stochastic evolutionary game dynamics, in the regime of replication-selection, reveals the emergence of spiteful behaviour as a dominant behaviour via a first order phase transition -- a discontinuous jump in the frequency of spiteful individuals at a threshold value of prejudicity. The phase transition is quite robust and becomes progressively conspicuous in the limit of large population size where deterministic evolutionary game dynamics, viz., replicator dynamics, approximates the system closely. The emergence of spite driven by prejudice is also found to persist when one considers long-term evolutionary dynamics in the mutation-selection dominated regime.

Problem

• Investigates prejudice-driven spite in ultimatum game interactions
• Models discontinuous phase transition in spiteful behavior emergence
• Analyzes evolutionary dynamics of prejudice intensity effects

Innovation

• Introducing prejudicity parameter in ultimatum game
• Revealing spite emergence via first-order phase transition
• Validating robustness through mutation-selection evolutionary dynamics