Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan.
Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines.
Sci Rep. 2022 May 19;12(1):8482. doi: 10.1038/s41598-022-12394-z.
The study of cooperation has been extensively studied in game theory. Especially, two-player two-strategy games have been categorized according to their equilibrium strategies and fully analysed. Recently, a grand unified game covering all types of two-player two-strategy games, i.e., the weightlifting game, was proposed. In the present study, we extend this two-player weightlifting game into an [Formula: see text]-player game. We investigate the conditions for pure strategy Nash equilibria and for Pareto optimal strategies, expressed in terms of the success probability and benefit-to-cost ratio of the weightlifting game. We also present a general characterization of [Formula: see text]-player games in terms of the proposed game. In terms of a concrete example, we present diagrams showing how the game category varies depending on the benefit-to-cost ratio. As a general rule, cooperation becomes difficult to achieve as group size increases because the success probability of weightlifting saturates towards unity. The present study provides insights into achieving behavioural cooperation in a large group by means of a cost-benefit analysis.
合作的研究在博弈论中得到了广泛的研究。特别是，根据其均衡策略对双人两策略博弈进行了分类，并进行了全面分析。最近，提出了一个涵盖所有类型的双人两策略博弈的大统一博弈，即举重博弈。在本研究中，我们将这个双人举重博弈扩展到了[公式：见正文]人游戏。我们研究了纯策略纳什均衡的条件和帕累托最优策略的条件，这些策略用举重博弈的成功概率和收益成本比来表示。我们还提出了一个用所提出的游戏来描述[公式：见正文]人游戏的一般特征。通过一个具体的例子，我们展示了图表，显示了游戏类别如何根据收益成本比而变化。一般来说，随着群体规模的增加，举重的成功概率趋于统一，合作变得更加困难。本研究通过成本效益分析，为在大群体中实现行为合作提供了思路。
