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ID: 608370.0, MPI für Evolutionsbiologie / Research Group Evolutionary Theory
On equilibrium properties of evolutionary multi-player games with random payoff matrices
Authors:Han, The Anh; Traulsen, Arne; Gokhale, Chaitanya S.
Language:English
Date of Publication (YYYY-MM-DD):2012-06
Title of Journal:Theoretical Population Biology
Volume:81
Issue / Number:4
Start Page:264
End Page:272
Review Status:not specified
Audience:Not Specified
Abstract / Description:The analysis of equilibrium points in biological dynamical systems has been of great interest in a variety of mathematical approaches to biology, such as population genetics, theoretical ecology or evolutionary game theory. The maximal number of equilibria and their classification based on stability have been the primary subjects of these studies, for example in the context of two-player games with multiple strategies. Herein, we address a different question using evolutionary game theory as a tool. If the payoff matrices are drawn randomly from an arbitrary distribution, what are the probabilities of observing a certain number of (stable) equilibria? We extend the domain of previous results for the two-player framework, which corresponds to a single diploid locus in population genetics, by addressing the full complexity of multiplayer games with multiple strategies. In closing, we discuss an application and illustrate how previous results on the number of equilibria, such as the famous Feldman–Karlin conjecture on the maximal number of isolated fixed points in a viability selection model, can be obtained as special cases of our results based on multi-player evolutionary games. We also show how the probability of realizing a certain number of equilibria changes as we increase the number of players and number of strategies.
Free Keywords:multi-player game theory; multiple strategies; number of equilibria; equilibrium stability
External Publication Status:published
Document Type:Article
Communicated by:Brigitte Lechner
Affiliations:MPI für Evolutionsbiologie/AG Evolutionstheorie
External Affiliations:Center of Artificial Intelligence, Department of Informatics, Faculty of Science and Technologies, New University of Lisbon, P-2829-516 Caparica, Portugal
Identifiers:ISSN:0040-5809 (print) [ID-No:1]
ISSN:1096-0325 (online) [ID-No:2]
DOI:10.1016/j.tpb.2012.02.004 [ID-No:3]
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