The survival of the weakest in a biased donation game
Chaoqian Wang, Jingyang Li, Xinwei Wang, Wenqiang Zhu, Attila Szolnoki

TL;DR
This study explores how biased Tit-for-Tat strategies influence cooperation dynamics in social dilemmas, revealing a counterintuitive 'survival of the weakest' phenomenon in structured populations.
Contribution
It introduces a biased Tit-for-Tat model with independent bias parameters, demonstrating complex phase behavior and the emergence of a 'hidden T phase' where weaker strategies dominate.
Findings
A 'hidden T phase' emerges with small T-bias and large C-bias.
Weaker T strategies can dominate due to non-transitive ecological mechanisms.
Structured populations are crucial for the observed phenomena.
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…
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