Information sharing between individuals is crucial to improve performance in collective tasks. However, in a competitive world, individuals may be reluctant to share information with the others, and it is still unclear how the presence of strategic behaviors affects the collective performance of a group. In this study, we introduce an evolutionary game modeling the dynamics of individual behaviors in a collective estimation task. The individuals are organized in a network and have to guess the distribution of ball colors in a box. Each of them samples a given number of balls and can strategically decide whether to share or not this information with its neighbors. We develop a framework that allows to investigate analytically how the collective performance depends on the network structure. We find that the optimal network results from a trade-off between the sharing rate and the way the information is integrated in the network. We further reveal that there exists an intermediate average degree for each type of network maximizing the collective performance. In addition to the uniform case, we consider the case of non-homogeneous allocations of the number of individual samples, showing that the largest collective performance is obtained when the number of ball extracted by an individual is inversely proportional to its degree.

翻译：个体间的信息共享对于提升集体任务中的绩效至关重要。然而，在竞争环境中，个体可能不愿意与他人分享信息，而策略行为如何影响群体的集体绩效仍不明确。本研究引入了一个演化博弈模型，用以模拟集体估计任务中的个体行为动态。个体被组织在网络中，需猜测盒中球颜色的分布。每个人抽取一定数量的球，并可以策略性地决定是否与邻居共享这些信息。我们开发了一个框架，能够从分析角度研究集体绩效如何依赖于网络结构。研究发现，最优网络源于共享率与信息在网络中整合方式之间的权衡。进一步揭示，每种类型的网络存在一个使集体绩效最大化的中间平均度数。除了均匀情况外，我们还考虑了非均匀分配个体样本数量的情形，结果表明，当个体抽取的球数与其度数成反比时，集体绩效达到最大。