2025/08/29 by Haoyu Yin, Xudong Chen, Yin, Haoyu +3
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Social Sciences · #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Electrical engineering #FOS: Mathematics #Game Theory and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2508.21299
openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when interacting with every other strategy, and it solely determines the replicator dynamics. If the payoff matrix is unknown, we show in this paper that it cannot be inferred from observed strategy frequencies alone -- distinct payoff matrices can induce the same replicator dynamics. We thus look for a canonical representative of the payoff matrix in the equivalence class. The main result of the paper is to show that for every polynomial replicator dynamics (i.e., the vector field is a polynomial), there always exists a skew-symmetric, polynomial payoff matrix that can induce the given dynamics.