The survival of the weakest in a biased donation game

2026-03-21

AI Summary

This study investigates how a biased Tit-for-Tat strategy (T) coexists with unconditional cooperators (C) and defectors in strong social dilemmas, giving rise to a “survival of the weakest” phenomenon. By constructing a three-player donation game model with an independent bias parameter that modulates T’s propensity to cooperate toward C and its own kind, the authors integrate evolutionary game theory, phase diagram analysis, and simulations in both structured and well-mixed populations. They reveal that when T exhibits weak cooperation bias toward its own type but strong bias toward C, a “hidden T phase” emerges in structured populations: despite having the lowest fitness, T achieves global dominance. This counterintuitive outcome arises because T attenuates C’s fitness advantage, thereby disrupting cyclic dominance clusters and highlighting the pivotal role of bias modulation in the evolution of cooperation.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Humans and AI: Learning Human Values and Preferences

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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Cooperating first then mimicking the partner's act has been proven to be effective in utilizing reciprocity in social dilemmas. However, the extent to which this, called Tit-for-Tat strategy, should be regarded as equivalent to unconditional cooperators remains controversial. Here, we introduce a biased Tit-for-Tat (T) strategy that cooperates differently toward unconditional cooperators (C) and fellow T players through independent bias parameters. The results show that, even under strong dilemmas in the donation game framework, this three-strategy system can exhibit diverse phase diagrams on the parameter plane. In particular, when T-bias is small and C-bias is large, a ``hidden T phase'' emerges, in which the weakest T strategy dominates. The dominance of the weakened T strategy originates from a counterintuitive mechanism characterizing non-transitive ecological systems: T suppresses its relative fitness to C, rapidly eliminates the cyclic dominance clusters, and subsequently expands slowly to take over the entire population. Analysis in well-mixed populations confirms that this phenomenon arises from structured populations. Our study thus reveals the subtle role of bias regulation in cooperative modes by emphasizing the ``survival of the weakest'' effect in a broader context.

Problem

• Tit-for-Tat
• donation game
• cooperation
• survival of the weakest
• biased strategy

Innovation

• biased Tit-for-Tat
• donation game
• survival of the weakest
• structured populations
• non-transitive dynamics