Differential game

Summary

A differential game is a game in which several players steer a common state through a control system. The state obeys a differential equation driven by all their controls. Each player has a cost or payoff that depends on the resulting trajectory, and the players have different goals. With one player it is an optimal control problem. The two-player zero-sum case leads to the Hamilton–Jacobi–Isaacs equation, and pursuit problems are the classical examples.