Differential game

In game theory, differential games are dynamic games that unfold in continuous time, meaning players’ actions and outcomes evolve smoothly rather than in discrete steps, and for which the rate of change of each state variable—like position, speed, or resource level—is governed by a differential equation. This distinguishes them from turn-based games (sequential games) like chess, focusing instead on real-time strategic conflicts.

Differential games are sometimes called continuous-time games, a broader term that includes them. While the two overlap significantly, continuous-time games also encompass models not governed by differential equations, such as those with stochastic jump processes, where abrupt, unpredictable events introduce discontinuities

Early differential games, often inspired by military scenarios, modeled situations like a pursuer chasing an evader, such as a missile targeting an aircraft. Today, they also apply to fields like economics and engineering, analyzing competition over resources or the control of moving systems.