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Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication

Banff International Research Station for Mathematical Innovation and Discovery

Human behavior can be modeled by describing, on a collective level, the adoption of certain strategies by individual agents. Many models use either the replicator dynamics (RD) or the logit formulation of the best-response (BR). How do RD and BR differ, and does the distinction matter This talk gives a brief overview of the two behavioral models, both of which originate from evolutionary game theory. Their differences are illustrated in the context of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by RD or BR. It will be shown that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in BR, the correspondence with RD decreases; the two model versions can differ substantially regarding the number of possible equilibria, the potential for multistability, and the type of sustained oscillations. Consequently, the choice of the behavioral model may profoundly affect the overall dynamics of a coupled human-environment system and deserves careful consideration. Joint work with Anthony Sun

Mathematics; Mathematics

video/mp4

Author affiliation: Osnabrück University

2021-07-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79085

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/