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Population Games on Dynamic Community Networks

Govaert, Alain LU ; Zino, Lorenzo and Tegling, Emma LU (2022) In IEEE Control Systems Letters 6. p.2695-2700
Abstract

In this letter, we deal with evolutionary game-theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities, in turn governed by an environmental feedback mechanism. When such a mechanism is independent of the game-theoretic learning process, a closed-loop system of differential equations is obtained. Through a direct analysis of the system, we study its asymptotic behavior. Specifically, we prove that, if the learning process converges, it converges to a (possibly restricted) Nash equilibrium... (More)

In this letter, we deal with evolutionary game-theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities, in turn governed by an environmental feedback mechanism. When such a mechanism is independent of the game-theoretic learning process, a closed-loop system of differential equations is obtained. Through a direct analysis of the system, we study its asymptotic behavior. Specifically, we prove that, if the learning process converges, it converges to a (possibly restricted) Nash equilibrium of the game, even when the dynamic flow process does not converge. Moreover, for a class of population games-two-strategy matrix games- a Lyapunov argument is employed to establish an evolutionary folk theorem that guarantees convergence to a subset of Nash equilibria, that is, the evolutionary stable states of the game. Numerical simulations are provided to illustrate and corroborate our findings.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Game theory, large-scale systems, network analysis and control
in
IEEE Control Systems Letters
volume
6
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85131344132
ISSN
2475-1456
DOI
10.1109/LCSYS.2022.3174916
project
Population Games in Dynamic Networked Environments
language
English
LU publication?
yes
id
60de0f32-905d-45b3-893b-a2f1cd0f4907
date added to LUP
2022-08-18 14:39:40
date last changed
2023-11-19 18:34:23
@article{60de0f32-905d-45b3-893b-a2f1cd0f4907,
  abstract     = {{<p>In this letter, we deal with evolutionary game-theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities, in turn governed by an environmental feedback mechanism. When such a mechanism is independent of the game-theoretic learning process, a closed-loop system of differential equations is obtained. Through a direct analysis of the system, we study its asymptotic behavior. Specifically, we prove that, if the learning process converges, it converges to a (possibly restricted) Nash equilibrium of the game, even when the dynamic flow process does not converge. Moreover, for a class of population games-two-strategy matrix games- a Lyapunov argument is employed to establish an evolutionary folk theorem that guarantees convergence to a subset of Nash equilibria, that is, the evolutionary stable states of the game. Numerical simulations are provided to illustrate and corroborate our findings.</p>}},
  author       = {{Govaert, Alain and Zino, Lorenzo and Tegling, Emma}},
  issn         = {{2475-1456}},
  keywords     = {{Game theory; large-scale systems; network analysis and control}},
  language     = {{eng}},
  pages        = {{2695--2700}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Control Systems Letters}},
  title        = {{Population Games on Dynamic Community Networks}},
  url          = {{http://dx.doi.org/10.1109/LCSYS.2022.3174916}},
  doi          = {{10.1109/LCSYS.2022.3174916}},
  volume       = {{6}},
  year         = {{2022}},
}