Evolutionary Game Theory: A Generalization of the ESS Definition

Elvio Accinelli, Filipe Martins and Jorge Oviedo
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Filipe Martins: Department of Mathematics, Faculdade de Ciências da, Universidade do Porto, Rua do Campo, Alegre, s/n, 4169-007 Porto, Portugal3Laboratório de Inteligência Artificial e, Apoio à Decisão (LIAAD), INESC TEC, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

International Game Theory Review (IGTR), 2019, vol. 21, issue 04, 1-19

Abstract: In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with n ≥ 3 players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with n ≥ 3 players. We show that unlike the case of n = 2, when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment.

Keywords: Evolutionary stable strategy; n-symmetric games; invasion barriers; local superior strategies; dynamic stability (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219198919500051

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