Calculus of Variations and Geometric Measure Theory

F. Bagagiolo - R. Capuani - L. Marzufero

A single player and a mass of agents: a pursuit-evasion like game

created by marzufero on 15 Feb 2023



Inserted: 15 feb 2023

Year: 2023

ArXiv: 2302.05742 PDF


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.

Keywords: viscosity solution, continuity equation, differential games, Mass transportation, Pursuit-evasion games, infinite-dimensional Isaacs equation, mean-field