2020/05/07 by Murat Arcak, Arcak, Murat, Nuno C. Martins +1 · 6 citations
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Electrical engineering #Mathematical and Theoretical Epidemiology and Ecology Models #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2005.03797
openalex publication_date 2020/05/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We analyze the stability of a nonlinear dynamical model describing the\nnoncooperative strategic interactions among the agents of a finite collection\nof populations. Each agent selects one strategy at a time and revises it\nrepeatedly according to a protocol that typically prioritizes strategies whose\npayoffs are either higher than that of the current strategy or exceed the\npopulation average. The model is predicated on well-established research in\npopulation and evolutionary games, and has two sub-components. The first is the\npayoff dynamics model (PDM), which ascribes the payoff to each strategy\naccording to the proportions of every population adopting the available\nstrategies. The second sub-component is the evolutionary dynamics model (EDM)\nthat accounts for the revision process. In our model, the social state at\nequilibrium is a best response to the payoff, and can be viewed as a Nash-like\nsolution that has predictive value when it is globally asymptotically stable\n(GAS). We present a systematic methodology that ascertains GAS by checking\nseparately whether the EDM and PDM satisfy appropriately defined\nsystem-theoretic dissipativity properties. Our work generalizes pioneering\nmethods based on notions of contractivity applicable to memoryless PDMs, and\nmore general system-theoretic passivity conditions. As demonstrated with\nexamples, the added flexibility afforded by our approach is particularly useful\nwhen the contraction properties of the PDM are unequal across populations.\n