Kinetic approach to the collective dynamics of the rock-paper-scissors binary game

Salvarani, Francesco; Pouradier Duteil, Nastassia

Salvarani, Francesco; Pouradier Duteil, Nastassia (2021), Kinetic approach to the collective dynamics of the rock-paper-scissors binary game, Applied Mathematics and Computation;0096-3003, 388. 10.1016/j.amc.2020.125496

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Type

Article accepté pour publication ou publié

Date

2021-01

Nom de la revue

Applied Mathematics and Computation;0096-3003

Volume

388

Éditeur

Elsevier

Identifiant publication

10.1016/j.amc.2020.125496

Métadonnées

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Auteur(s)

Salvarani, Francesco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dipartimento di matematica F. Casorati
Pouradier Duteil, Nastassia
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]

Résumé (EN)

This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.