We study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and the exit cost consists of three different exit costs, depending whether either the first player only leaves its domain, or the second player only leaves its domain, or they both simultaneously leave their own domain. We prove that, under suitable hypotheses, the lower and upper values are continuous and are, respectively, the unique viscosity solution of a suitable Dirichlet problem for a Hamilton–Jacobi–Isaacs equation. The continuity of the values relies on the existence of suitable non-anticipating strategies respecting the domain constraint. This problem is also treated in this work. Introduction

A differential game with exit costs / Bagagiolo, Fabio; Maggistro, Rosario; Zoppello, Marta. - In: DYNAMIC GAMES AND APPLICATIONS. - ISSN 2153-0785. - STAMPA. - 2020,10:2(2020), pp. 297-327. [10.1007/s13235-019-00334-y]

### A differential game with exit costs

#### Abstract

We study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and the exit cost consists of three different exit costs, depending whether either the first player only leaves its domain, or the second player only leaves its domain, or they both simultaneously leave their own domain. We prove that, under suitable hypotheses, the lower and upper values are continuous and are, respectively, the unique viscosity solution of a suitable Dirichlet problem for a Hamilton–Jacobi–Isaacs equation. The continuity of the values relies on the existence of suitable non-anticipating strategies respecting the domain constraint. This problem is also treated in this work. Introduction
##### Scheda breve Scheda completa Scheda completa (DC)
2020
2
Bagagiolo, Fabio; Maggistro, Rosario; Zoppello, Marta
A differential game with exit costs / Bagagiolo, Fabio; Maggistro, Rosario; Zoppello, Marta. - In: DYNAMIC GAMES AND APPLICATIONS. - ISSN 2153-0785. - STAMPA. - 2020,10:2(2020), pp. 297-327. [10.1007/s13235-019-00334-y]
File in questo prodotto:
File
Bagagiolo_Maggistro_Zoppello_newsubmission_revised_25_august_2019.pdf

Solo gestori archivio

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 404.9 kB
Formato Adobe PDF
Bagagiolo2019_Article_ADifferentialGameWithExitCosts.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 671.15 kB
Formato Adobe PDF

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/11572/243732`
• ND
• 4
• 5