The survival of the weakest in a biased donation game

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.

11 pages, 5 figures, accepted for publication in Applied Mathematics and Computation

References in corpus (11)

• Statistical physics of human cooperation
• Reward and cooperation in the spatial public goods game
• Cyclic dominance in evolutionary games: A review
• Phase diagrams for three-strategy evolutionary prisoner's dilemma games on regular graphs
• Costly hide and seek pays: Unexpected consequences of deceit in a social dilemma
• Early exclusion leads to cyclical cooperation in repeated group interactions
• Strategy dependent learning activity in cyclic dominant systems
• Competition of alliances in a cyclically dominant eight-species population
• Public goods games on any population structure
• Evolution of cooperation and competition in multilayer networks
• When faster rotation is harmful: the competition of alliances with inner blocking mechanism