Playable differential games

Playability conditions of differential games are studied by using Viability Theory. First, the results on payability of time independent differential games are extended to time dependent games. In fact, time is introduced in the dynamics of the game, in the state dependent constraints bearing on controls, and in state constraints. Second, some examples of pursuit games are studied. Necessary and sufficient conditions of playability of the game are provided. Here, pursuit games are directly considered as “games of kind” (in Isaacs's sense) and are not considered as “games of degree.” The viability condition does not always provide the “optimal strategy” to be as close as possible to a certain goal, but it supplies strategies allowing the system to reach a given goal