Rowlett J, Karlsson C J, Nursultanov M
Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, 41296 Gothenburg, Sweden.
Department of Mathematics and Statistics, University of Helsinki, PO Box 68, Helsinki FI-00014, Finland.
R Soc Open Sci. 2022 Aug 10;9(8):211916. doi: 10.1098/rsos.211916. eCollection 2022 Aug.
How does the composition of a collection of individuals affect its outcome in competition with other collections of individuals? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level consequences. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms and finance. Our first main contribution is a game theoretic model that interpolates between the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing diversity due to the strength it imparts to the system in competition with others.
一群个体的组成如何影响其在与其他个体群体竞争中的结果？假设个体可以存在差异，我们开发了一个模型来在个体层面的相互作用和集体层面的结果之间进行插值。该模型基于理论数学，不受任何特定背景的限制。潜在应用包括研究、教育、体育、政治、生态、农业、算法和金融。我们的第一个主要贡献是一个博弈论模型，它在一群个体的内部组成与该群体作为一个整体在与其他群体竞争时的影响之间进行插值。第二个主要贡献是对所有平衡点和策略的严格识别。这些平衡点表明，由于生物和物理系统在与其他系统竞争时赋予系统的力量，它们倾向于增加多样性的一种机制基础。
