CWRU MAMS PhD alumnus Alex Strang and CWRU faculty Karen Abbott (BIOL) and Peter Thomas (MAMS) published an article on “The Network HHD: Quantifying Cyclic Competition in Trait-Performance Models of Tournaments” in the May, 2022 issue of the prestigious journal Society for Industrial and Applied Mathematics Review.  

A tournament is intransitive, or cyclic, if it contains rock-paper-scissors cycles, i.e. competitors A, B and C such that A typically defeats B, B typically defeats C, but C typically defeats A.  Real-world examples arise in sports, politics, population ecology, and animal behavior. The paper applies statistical tools to quantify the expected degree of intransitivity when competitive outcomes are determined by randomly sampled competitor traits. The paper proves intuitive statements relating the degree of cyclicity to simple correlations in competitor performance and the tournament size. For example, it is shown that the more an agent’s performance depends on their opponent, the more cyclic the tournament on average. Link: https://epubs.siam.org/doi/10.1137/20M1321012