Abstract
The chapter is devoted to two-player, zero-sum differential games, with a special emphasis on the existence of a value and its characterization in terms of a partial differential equation, the Hamilton-Jacobi-Isaacs equation. We discuss different classes of games: in finite horizon, in infinite horizon, and pursuit-evasion games. We also analyze differential games in which the players do not have a full information on the structure of the game or cannot completely observe the state. We complete the chapter by a discussion on differential games depending on a singular parameter: for instance, we provide conditions under which the differential game has a long-time average.
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Notes
- 1.
Unless one allows an information advantage to one player, amounting to letting him know his opponent’s control at each time (Krasovskii and Subbotin 1988).
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Cardaliaguet, P., Rainer, C. (2018). Zero-Sum Differential Games. In: Başar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-44374-4_4
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DOI: https://doi.org/10.1007/978-3-319-44374-4_4
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