Population Games on Dynamic Community Networks
(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
- Govaert, Alain LU ; Zino, Lorenzo and Tegling, Emma LU
- organization
- publishing date
- 2022
- 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}}, }