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

Imitation dynamics in population games on community networks / Como, Giacomo; Fagnani, Fabio; Zino, Lorenzo. - In: IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS. - ISSN 2325-5870. - ELETTRONICO. - 8:1(2021), pp. 65-76. [10.1109/TCNS.2020.3032873]

Imitation dynamics in population games on community networks

Como, Giacomo;Fagnani, Fabio;Zino, Lorenzo
2021

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 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
File in questo prodotto:
File Dimensione Formato  
cfz_imitation_tcns_finale.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 645.99 kB
Formato Adobe PDF
645.99 kB Adobe PDF Visualizza/Apri
Imitation_Dynamics_in_Population_Games_on_Community_Networks.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 643.85 kB
Formato Adobe PDF
643.85 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2851212