Work

On zero-sum game representation for replicator dynamics

Year: 2025

Type: article

Abstract: 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.

Source: Systems & Control Letters

DOI: 10.1016/j.sysconle.2025.106326

Authors: Haoyu Yin, Xudong Chen, Bruno Sinopoli

Institution: Washington University in St. Louis

Language: English

Topic: Evolutionary Game Theory and Cooperation

Subfield: Sociology and Political Science

Field: Social Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,910

Funder: National Science Foundation