| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2024009 | |
| Published online | 07 March 2024 | |
A single player and a mass of agents: A pursuit evasion-like game
1
University of Trento, Department of Mathematics,
Via Sommarive 14,
38123
Povo
(TN),
Italy
2
University of Arizona, Department of Mathematics,
617 N. Santa Rita Ave.,
Tucson,
USA
3
“La Sapienza” University of Rome, Department of Basic and Applied Sciences for Engineering,
Via Antonio Scarpa 16,
00161
Rome
(RM),
Italy
* Corresponding author: luciano.marzufero@gmail.com
Received:
11
February
2023
Accepted:
24
January
2024
We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport equation type. Using also an adapted concept of non-anticipating strategies, we derive an infinite dimensional Isaacs equation, and by dynamic programming techniques we prove that the value function is the unique viscosity solution on a suitable invariant subset of a Hilbert space.
Mathematics Subject Classification: 49N70 / 49N75 / 49L12 / 49L25 / 49N80 / 35Q49
Key words: Pursuit-evasion games / differential games / infinite-dimensional Isaacs equation / continuity equation / mass transportation / mean-field / viscosity solution
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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