A game set in continuous time with the change in the state variable determined by the strategies of the two players. Let time be denoted by t and the state of the system at time t by x(t). Assume there are two players. If player 1 chooses the strategy u(t) and player 2 chooses strategy v(t) then the change in the state, $\dot{x}(t)$, is governed by the differential equation $\dot{x}(t)=f(x(t)\text{,}u(t)\text{,}v(t))$. The pay-offs to the two players are determined by the state of the system. See also Optimal Control.