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  "body": "\n## Summary\n\nA differential game is a game in which several players steer a common state through a [[control system|ZPDTVZQN5K]].\nThe state obeys a differential equation driven by all their controls.\nEach player has a cost or payoff that depends on the resulting trajectory, and the players have different goals.\nWith one player it is an [[optimal control|T3V6ZNAMDN]] problem.\nThe two-player zero-sum case leads to the [[Hamilton–Jacobi–Isaacs equation|WHTBZ3K4FB]], and pursuit problems are the classical examples.\n\n## Explanations\n\n### L1 human\n\nPicture a cat chasing a mouse in a field.\nBoth move continuously, and each changes direction at every instant in reaction to the other.\nThe cat wants to catch the mouse quickly, the mouse wants to escape or at least delay capture.\nA differential game is the mathematical model of such a contest: the positions obey differential equations, and each player chooses its control as time runs.\nIn a simple version, both move in the plane with bounded speed, the cat faster, and the payoff is the time to capture.\n",
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