Zero-Sum Differential Games

Pierre Cardaliaguet () and Catherine Rainer ()
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Pierre Cardaliaguet: Université Paris-Dauphine
Catherine Rainer: Université de Brest, Département, Laboratoire de Mathématiques LMBA

Chapter 8 in Handbook of Dynamic Game Theory, 2018, pp 373-430 from Springer

Abstract: 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.

Keywords: Differential games; Zero-sum games; Viscosity solutions; Hamilton-Jacobi equations; Bolza problem; Pursuit-evasion games; Search games; Incomplete information; Long-time average; Homogenization (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-44374-4_4

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