多样性的力量：由可变个体组成的集合在面对挑战时具有鲁棒性的数学证明
The strength of diversity: mathematical proof that collections of variable individuals are robust in the face of challenges
AI总结：
本文通过博弈论框架和均衡分析，从数学上证明了个体多样性能够增强系统在竞争中的鲁棒性，为生物和物理系统趋向复杂性和熵增提供了机制性解释。
摘要：
能否证明由不同个体组成的系统中，多样性对整个系统性能的定量影响？假设个体可以不同，我们开发了一个模型，在个体层面的相互作用与集体层面的影响之间进行插值。该模型植根于理论数学，不受任何特定情境的限制。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框架，用于进一步分析个体集合的内部构成及其在与其他集合竞争时对整个集合的影响。第二个主要贡献是对所有均衡点和策略的严格识别。这些均衡表明，生物和物理系统趋向于增加复杂性和熵具有机制性基础，因为多样性在与他人竞争中赋予系统力量。
英文摘要：
Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level ramifications. 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 framework for further analysis of 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 complexity and entropy, because diversity imparts strength to a system in competition with others.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
