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Can one demonstrate quantitative effects of diversity within a systemcomprised of distinct individuals on the performance of the system as a whole?Assuming that individuals can be different, we develop a model to interpolatebetween individual-level interactions and collective-level ramifications.Rooted in theoretical mathematics, the model is not constrained to any specificcontext. Potential applications include research, education, sports, politics,ecology, agriculture, algorithms, and finance. Our first main contribution is agame theoretic framework for further analysis of the internal composition of anensemble of individuals and the repercussions for the ensemble as a whole incompetition with others. The second main contribution is the rigorousidentification of all equilibrium points and strategies. These equilibriasuggest a mechanistic underpinning for biological and physical systems to tendtowards increasing complexity and entropy, because diversity imparts strengthto a system in competition with others.

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