Title: A reversed form of public goods game: equivalence and difference Show Chinese title

Title: 公共物品博弈的反向形式：等价与差异

Abstract: According to the public goods game (PGG) protocol, participants decide freely whether they want to contribute to a common pool or not, but the resulting benefit is distributed equally. A conceptually similar dilemma situation may emerge when participants consider if they claim a common resource but the related cost is covered equally by all group members. The latter establishes a reversed form of the original public goods game (R-PGG). In this work, we show that R-PGG is equivalent to PGG in several circumstances, starting from the traditional analysis, via the evolutionary approach in unstructured populations, to Monte Carlo simulations in structured populations. However, there are also cases when the behavior of R-PGG could be surprisingly different from the outcome of PGG. When the key parameters are heterogeneous, for instance, the results of PGG and R-PGG could be diverse even if we apply the same amplitudes of heterogeneity. We find that the heterogeneity in R-PGG generally impedes cooperation, while the opposite is observed for PGG. These diverse system reactions can be understood if we follow how payoff functions change when introducing heterogeneity in the parameter space. This analysis also reveals the distinct roles of cooperator and defector strategies in the mentioned games. Our observations may hopefully stimulate further research to check the potential differences between PGG and R-PGG due to the alternative complexity of conditions. Show Chinese abstract

Abstract: 根据公共物品博弈（PGG）协议，参与者可以自由决定是否要向一个共同池子做出贡献，但产生的利益会被平均分配。 当参与者考虑是否索取一种公共资源时，可能会出现概念上类似的困境，但相关的成本由所有组成员平均承担。 后者建立了一种原始公共物品博弈的反向形式（R-PGG）。 在本工作中，我们表明在几种情况下，R-PGG与PGG是等价的，从传统的分析开始，经过无结构种群中的进化方法，再到结构化种群中的蒙特卡洛模拟。 然而，也存在一些情况，R-PGG的行为可能与PGG的结果出人意料地不同。 当关键参数是异质的时候，例如，即使我们应用相同程度的异质性幅度，PGG和R-PGG的结果也可能多种多样。 我们发现，R-PGG中的异质性通常会阻碍合作，而在PGG中则观察到相反的情况。 如果我们跟踪收益函数在参数空间中引入异质性时的变化方式，就可以理解这些不同的系统反应。 这一分析还揭示了在上述游戏中合作者和背叛者策略的不同作用。 我们的观察结果可能有望激发进一步的研究，以检查由于条件复杂性的不同而可能导致的PGG和R-PGG之间的潜在差异。