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Erschienen in: Dynamic Games and Applications 1/2018

20.10.2016

State-Policy Dynamics in Evolutionary Games

verfasst von: Ilaria Brunetti, Yezekael Hayel, Eitan Altman

Erschienen in: Dynamic Games and Applications | Ausgabe 1/2018

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Abstract

Standard evolutionary game theory framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the policies and the individual states inside a population of interacting individuals. We first define a general model by coupling replicator dynamics and continuous-time Markov decision processes, and we then consider a particular case of a two policies and two states evolutionary game. We first obtain a system of combined dynamics, and we show that the rest points of this system are equilibria profiles of our evolutionary game with individual state dynamics. Second, by assuming two different timescales between states and policies dynamics, we can compute explicitly the equilibria. Then, by transforming our evolutionary game with individual states into a standard evolutionary game, we obtain an equilibrium profile which is equivalent, in terms of occupation measures and expected fitness to the previous one. All our results are illustrated with numerical analysis.

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Metadaten
Titel
State-Policy Dynamics in Evolutionary Games
verfasst von
Ilaria Brunetti
Yezekael Hayel
Eitan Altman
Publikationsdatum
20.10.2016
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 1/2018
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-016-0208-0

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