A zero-sum differential game for two opponent masses

Fabio Bagagiolo (), Rossana Capuani () and Luciano Marzufero ()
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Fabio Bagagiolo: University of Trento
Rossana Capuani: University of Arizona
Luciano Marzufero: Free University of Bozen-Bolzano

Partial Differential Equations and Applications, 2025, vol. 6, issue 3, 1-23

Abstract: 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 velocity vector 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: Zero-sum games; Differential games; Infinite-dimensional Isaacs equation; Mass transportation; Viscosity solutions; Primary 49N70; Secondary 49N75; 49L12; 49L25; 35Q49 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00322-5

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