Attila Szolnoki

Chaoqian Wang, Jingyang Li, Xinwei Wang et al.

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.

Bin Pi, Minyu Feng, Liang-Jian Deng et al.

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic properties in structured populations, derive theoretical conditions for cooperation, and identify the optimal game distribution for promoting cooperation. To address these issues, we propose the variable game framework in a structured population, where the game interactions between different individuals change over time. By means of the Markov chain and the pair approximation method, we derive theoretical conditions under which cooperation is favored by natural selection and when it is favored over defection under weak selection. Furthermore, we respectively formulate and solve two optimization problems to determine the optimal game distribution that most effectively fosters the evolution of cooperation by maximizing the gradient of cooperation selection and minimizing the fitness difference between defectors and cooperators. The theoretical predictions regarding both the conditions for cooperation and optimal game distribution are further validated by numerical calculations and extensive Monte Carlo simulations. Our findings offer novel insights into the mechanisms driving cooperative behavior in complex systems and provide theoretical guidance for designing optimal game environments that facilitate the evolution of cooperation.

Qin Li, Ting Ling, Minyu Feng et al.

Taxation constitutes a fundamental component of modern national economic systems, exerting profound impacts on both societal functioning and governmental operations. In this paper, we employ an interdependent network approach to model the coevolution between citizens and regulators within a taxation system that fundamentally constitutes a public goods game framework with complex interactive dynamics. In a game layer, citizens engage in public goods games, facing the social dilemma of tax compliance (cooperation) versus evasion (defection). Tax compliance supports the sustainability of public finances while tax evasion presents markedly stronger short-term incentives. In a regulatory layer, fair regulators punish tax evaders, while corrupt regulators keep silent due to bribes. Governmental regulatory interventions introduce critical institutional constraints that alter the traditional equilibrium of the game. Importantly, there exists a strategy update not only among citizens but also among regulators. Our results indicate that strengthening penalties can effectively curb tax evasion, and the influence of bribery on both tax compliance rates and the proportion of fair regulators is nonlinear. Additionally, increasing regulators' salaries and intensifying the crackdown on corrupt regulators can foster the emergence of fair regulators, thereby reducing tax evasion among citizens. The results offer practical policy implications, suggesting that balanced deterrence and institutional fairness are essential to sustaining compliance, and point to the need for future empirical validation and model extensions.

Marcos Cardinot, Colm O'Riordan, Josephine Griffith et al.

It is generally believed that in a situation where individual and collective interests are in conflict, the availability of optional participation is a key mechanism to maintain cooperation. Surprisingly, this effect is sensitive to the use of microscopic dynamics and can easily be broken when agents make a fully rational decision during their strategy updates. In the framework of the celebrated prisoner's dilemma game, we show that this discrepancy can be fixed automatically if we leave the strict and frequently artifact condition of a fully occupied interaction graph, and allow agents to change not just their strategies but also their positions according to their success. In this way, a diluted graph where agents may move offers a natural and alternative way to handle artifacts arising from the application of specific and sometimes awkward microscopic rules.