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

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
Journal name
Applied Mathematics and Computation;0096-3003
Volume
388
Publisher
Elsevier
Publication identifier
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Author(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)]
Abstract (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.
Subjects / Keywords
Kinetic Equations; Binary games; Diffusion limits