Chapter 22 Differential games This chapter discusses differential games. In control theory a certain evolutionary process (typically given by a time dependent system of differential equations) depends on a control variable. A certain cost is associated with the control variable and with the corresponding evolutionary process. The goal is to choose the best controlthat is the control for which the cost is minimized. A similar evolutionary process is used in differential games but it depends on two (or more) controls. Each player is in charge of one of the controls. Each player wishes to minimize its own cost (the cost functions of the different players may be related). However at each time t a player must decide on its control without knowing what the other (usually opposing) players intend to do. The strategy of each player at time t depends only on whatever information the player was able to gain by observing the evolving process up to time t only.