A zero-sum differential game for two opponent masses
Optimization and Control
2025-05-07 v2
Abstract
We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity equation, where the control is given by the vector velocity field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.
Keywords
Cite
@article{arxiv.2408.03860,
title = {A zero-sum differential game for two opponent masses},
author = {Fabio Bagagiolo and Rossana Capuani and Luciano Marzufero},
journal= {arXiv preprint arXiv:2408.03860},
year = {2025}
}