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Network imitation dynamics in population games on community networks

Como, Giacomo LU ; Fagnani, Fabio and Zino, Lorenzo (2020) In IEEE Transactions on Control of Network Systems
Abstract

We study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism --- encompassing the replicator dynamics --- is that players belonging to a single population exchange information through pairwise interactions, whereby they get aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating the one of the players they interact with. The pattern of interactions regulating the learning process is determined by a community structure. First, the set of equilibrium points of such network imitation dynamics is characterized. Second, for the class of... (More)

We study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism --- encompassing the replicator dynamics --- is that players belonging to a single population exchange information through pairwise interactions, whereby they get aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating the one of the players they interact with. The pattern of interactions regulating the learning process is determined by a community structure. First, the set of equilibrium points of such network imitation dynamics is characterized. Second, for the class of potential games and for undirected and connected community networks, global asymptotic convergence is proved. In particular, our results guarantee convergence to a Nash equilibrium from every fully supported initial population state in the special case when the Nash equilibria are isolated and fully supported. Examples and numerical simulations are offered to validate the theoretical results and counterexamples are discussed for scenarios when the assu

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type
Contribution to journal
publication status
in press
subject
keywords
Asymptotic stability, Convergence, Distributed Learning, Evolutionary Game Theory, Games, Imitation Dynamics, Learning systems, Network Systems, Population Games, Sociology, Stability analysis, Statistics
in
IEEE Transactions on Control of Network Systems
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85096087774
ISSN
2325-5870
DOI
10.1109/TCNS.2020.3032873
project
Modeling and Control of Large Scale Transportation Networks
language
English
LU publication?
no
id
897d1ac9-f667-4c36-90b8-2f563c7039c5
date added to LUP
2021-02-08 22:55:52
date last changed
2021-02-18 13:33:51
@article{897d1ac9-f667-4c36-90b8-2f563c7039c5,
  abstract     = {<p>We study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism --- encompassing the replicator dynamics --- is that players belonging to a single population exchange information through pairwise interactions, whereby they get aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating the one of the players they interact with. The pattern of interactions regulating the learning process is determined by a community structure. First, the set of equilibrium points of such network imitation dynamics is characterized. Second, for the class of potential games and for undirected and connected community networks, global asymptotic convergence is proved. In particular, our results guarantee convergence to a Nash equilibrium from every fully supported initial population state in the special case when the Nash equilibria are isolated and fully supported. Examples and numerical simulations are offered to validate the theoretical results and counterexamples are discussed for scenarios when the assu</p>},
  author       = {Como, Giacomo and Fagnani, Fabio and Zino, Lorenzo},
  issn         = {2325-5870},
  language     = {eng},
  publisher    = {IEEE - Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Control of Network Systems},
  title        = {Network imitation dynamics in population games on community networks},
  url          = {http://dx.doi.org/10.1109/TCNS.2020.3032873},
  doi          = {10.1109/TCNS.2020.3032873},
  year         = {2020},
}