On the one-dimensional mean-field games with congestion

• Autorzy: Sedjro Marc

Identyfikatory

DOI

10.14708/ma.v50i1.7136

Warianty tytułu

PL

O modelach gier uśrednionego oddziaływania z zarządzaniem

• Języki publikacji: EN

Abstrakty

EN

In this work, we consider a one dimensional forward-forward model of Mean-field Games with congestion. We establish a connection between such models and conservation laws. Next, we show the existence of a non trivial convex entropies. Finally, we investigate the existence of solutions in the parabolic case and derived some estimates thanks to the existence of such convex entropies.

PL

Praca poświęcona jest jednowymiarowym modelom gier z uśrednionym oddziaływaniem w zarządzaniu. Takie badania mają na celu analizę podejmowania strategicznych decyzji przez czynniki mało oddziaływające w bardzo dużych populacjach. Ustalany jest związek między takimi modelami a prawami zachowania. W wyniku tych badań pokazano istnienie nietrywialnych entropii wypukłych. W końcowej części badane jest istnienie rozwiązań w przypadku parabolicznym i wyprowadzane są pewne oszacowania z istnienia takich wypukłych entropii.

Słowa kluczowe

EN

mean-field games; systems of conservation laws; Hamilton-Jacobi equations; transport equation; Fokker-Planck equation

PL

równanie Fokkera-Plancka; równanie Hamiltona-Jacobiego; gry z uśrednionym oddziaływaniem; prawa zachowania; wypukła entropia

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2022
• Tom: Vol. 50, no. 1
• Strony: 139--151
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Sedjro Marc

• Humboldt University Berlin, Germany

• https://orcid.org/0000-0003-3574-1274

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).