The value of a zero-sum differential games is known to exist, under Isaacs’ condition, and it is the unique viscosity solution of a Hamilton-Jacobi-Isaacs equation. This approach, in spite of being very effective, does not provide information about the strategies the players should use. In this note we provide a self-contained proof of the existence of the value based on the construction of ε-optimal strategies, which is inspired by the “extremal aiming” method from [5].

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