The conflict between individual and collective interests makes fostering cooperation in human societies a challenging task, requiring drastic measures such as the establishment of sanctioning institutions. These institutions are costly because they have to be maintained regardless of the presence or absence of offenders. Here, we revisit some improvements to the standard N-person prisoner's dilemma formulation with institutional punishment in a well-mixed population, namely the elimination of overpunishment, the requirement of a minimum number of contributors to establish the sanctioning institution, and the sharing of its maintenance costs once this minimum number is reached. In addition, we focus on large groups or communities for which sanctioning institutions are ubiquitous. Using the replicator equation framework for an infinite population, we find that by sufficiently fining players who fail to contribute either to the public good or to the sanctioning institution, a population of contributors immune to invasion by these free riders can be established, provided that the contributors are sufficiently numerous. In a finite population, we use finite-size scaling to show that, for some parameter settings, demographic noise helps to fixate the strategy that contributes to the public good but not to the sanctioning institution even for infinitely large populations when, somewhat counterintuitively, its proportion in the initial population vanishes with a small power of the population size.

Bianca Y S Ishikawa

José F Fontanari

Theory in Biosciences

生物科学理论侧重于理论生物学的新概念。它还包括分析和建模方法以及哲学和历史问题。中心主题是：人工生命；关注新方法、现象和解释的生物信息学；仿生建模；复杂性、稳健性和弹性；具身认知；进化生物学；EVO-DEVO；博弈论建模；遗传学；生物学史；语言进化；数学生物学；生命起源；生物学哲学；种群生物学；系统生物学；理论生态学；理论分子生物学；理论神经科学与认知。

The journal "Theory in Biosciences" focuses on new concepts in theoretical biology. It encompasses analytical and modeling methods, as well as philosophical and historical issues. The central themes include: artificial life; new methods, phenomena, and explanations in bioinformatics; biomimetic modeling; complexity, robustness, and resilience; embodied cognition; evolutionary biology; EVO-DEVO; game-theoretic modeling; genetics; history of biology; language evolution; mathematical biology; origin of life; philosophy of biology; population biology; systems biology; theoretical ecology; theoretical molecular biology; theoretical neuroscience and cognition.

《Theory in Biosciences》期刊专注于理论生物学的新概念，涵盖分析与建模方法，以及相关的哲学和历史问题。主要主题包括：人工生命；生物信息学的新方法、现象和解释；仿生建模；复杂性、稳健性和弹性；具身认知；进化生物学；EVO-DEVO；博弈论建模；遗传学；生物学史；语言进化；数学生物学；生命起源；生物学哲学；种群生物学；系统生物学；理论生态学；理论分子生物学；理论神经科学与认知。

Category	Quartile
生物学	4
生物学, 生物学	4
生物学, 数学与计算生物学	4

Revisiting institutional punishment in the N-person prisoner’s dilemma

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Category	Quartile
MATHEMATICAL & COMPUTATIONAL BIOLOGY	4