Meloni Sandro, Xia Cheng-Yi, Moreno Yamir
Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain; Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain.
Key Laboratory of Computer Vision and System (Ministry of Education) and Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology , Tianjin University of Technology , Tianjin 300384, People's Republic of China.
R Soc Open Sci. 2017 Mar 8;4(3):170092. doi: 10.1098/rsos.170092. eCollection 2017 Mar.
Public goods games (PGGs) represent one of the most useful tools to study group interactions. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution-known as Pareto Law-and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of PGGs that allows for the emergence of both of these features from first principles. Unlike traditional PGGs, where players contribute equally to all the games in which they participate, we allow individuals to redistribute their contribution according to what they earned in previous rounds. Results from numerical simulations show that not only a Pareto distribution for the pay-offs naturally emerges but also that if players do not invest enough in one round they can act as defectors even if they are formally cooperators. Our results not only give an explanation for wealth heterogeneity observed in real data but also point to a conceptual change on cooperation in collective dilemmas.
公共物品博弈（PGGs）是研究群体互动最有用的工具之一。然而，即使它们能够为现代社会中合作的出现和稳定提供一种解释，但它们无法重现一些在社会和经济互动中观察到的关键特征。财富分配的典型形态——即所谓的帕累托法则——以及财富生产的微观组织就是其中两个特征。在此，我们对公共物品博弈的经典形式进行了修改，使得这两个特征能够从第一原理中出现。与传统的公共物品博弈不同，在传统博弈中玩家对他们参与的所有博弈贡献相同，我们允许个体根据他们在前几轮中的所得来重新分配他们的贡献。数值模拟结果表明，不仅收益的帕累托分布自然出现，而且如果玩家在某一轮中投资不足，即使他们在形式上是合作者，他们也可能表现得像背叛者。我们的结果不仅为实际数据中观察到的财富异质性提供了解释，还指出了集体困境中合作观念的转变。
