The strength of diversity: mathematical proof that collections of variable individuals are robust in the face of challenges

TL;DR

This paper presents a mathematical model demonstrating that diversity among individuals enhances the robustness and performance of systems across various fields, supported by game theory and equilibrium analysis.

Contribution

It introduces a novel game theoretic framework and rigorously identifies all equilibrium points, linking diversity to system strength and complexity.

Findings

Diversity increases system robustness against challenges.

Equilibrium analysis reveals strategies that favor diverse compositions.

Systems tend toward higher complexity and entropy due to diversity.

Abstract

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.