| Issue |
EPL
Volume 146, Number 4, May 2024
|
|
|---|---|---|
| Article Number | 47001 | |
| Number of page(s) | 4 | |
| Section | Biological and soft matter physics | |
| DOI | https://doi.org/10.1209/0295-5075/ad473e | |
| Published online | 31 May 2024 | |
Imitation dynamics and the replicator equation
Instituto de Física de São Carlos, Universidade de São Paulo - Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
Received: 31 March 2024
Accepted: 3 May 2024
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the central equation of this theory —the replicator equation— is the deterministic limit of a stochastic imitation (social learning) dynamics. Here we offer an alternative elementary proof of this result, which holds for the scenario where players compare their instantaneous (not average) payoffs to decide whether to maintain or change their strategies, and only more successful individuals can be imitated.
© 2024 EPLA
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