Random information horizon for a class of differential games with continuous updating

In the paper we consider a class of the differential games with continuous updating with random information horizon. It is assumed that at each time instant, players have information about the game (motion equations and payoff functions) for a time interval with the length $\theta$ and as the time evolves information about the game updates. We first considered this type of games in 2019. Here we additionally assume that $\theta$ is a random variable. The subject of the current paper is definition of Nash equilibrium based solution concept and solution technique based on Hamilton — Jacobi — Bellman equations.