Calculus of Variations and Geometric Measure Theory

C. Jimenez

A Zero Sum Differential Game With Correlated Informations on the Initial Position. A case with a continuum of initial positions.

created by jimenez on 09 Feb 2021


Accepted Paper

Inserted: 9 feb 2021
Last Updated: 9 feb 2021

Journal: Journal of Dynamics and Games
Year: 2021


We study a two player zero sum game where the initial position $z_0$ is not communicated to any player. The initial position is a function of a couple $(x_0,y_0)$ where $x_0$ is communicated to player I while $y_0$ is communicated to player II. The couple $(x_0,y_0)$ is chosen according a probability measure $dm(x,y)=h(x,y) d\mu(x) d\nu(y)$. We show that the game has a value and, under additional regularity assumptions, that the value is a solution of Hamilton Jacobi Isaacs equation in a dual sense.