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.

翻译：先合作后模仿伙伴行为已被证明在社会困境中有效利用互惠机制。然而，这种被称为"以牙还牙"策略与无条件合作者等价的程度仍存在争议。本文引入一种偏向性以牙还牙（T）策略，通过独立偏置参数对无条件合作者（C）和同类T玩家采取不同合作程度。结果表明，即使在捐赠博弈框架下的强困境中，该三策略系统也能在参数平面上呈现多样化相图。特别地，当T偏置较小而C偏置较大时，会出现"隐藏T相"，其中最弱T策略占据主导地位。这种弱化T策略的主导地位源于表征非传递生态系统的反直觉机制：T策略通过抑制自身对C的相对适应度，快速消除循环主导簇，随后缓慢扩张直至占领整个种群。充分混合种群分析证实该现象源于结构化种群。本研究通过揭示更广泛背景下"最弱者生存"效应，阐明了合作模式中偏置调节的微妙作用。