Hamilton–Jacobi–Isaacs equation

Summary

The Hamilton–Jacobi–Isaacs equation is the partial differential equation for the value of a two-player zero-sum differential game. It is the analogue for games of the Hamilton–Jacobi–Bellman equation of optimal control, with a min-max in place of a minimum. Under standard hypotheses the upper and lower values of the game are its viscosity solutions. When the min and the max commute, the game has a value and the equation characterises it.