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arXiv · 2302.05742

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

Fabio Bagagiolo·Rossana Capuani·Luciano Marzufero
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Abstract

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.

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Fabio Bagagiolo, Rossana Capuani, Luciano Marzufero. 2023-02-11. A single player and a mass of agents: a pursuit evasion-like game. https://doi.org/10.1051/cocv%2F2024009

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