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Zero-Sum Differential Games

  • Pierre Cardaliaguet
  • Catherine Rainer
Reference work entry

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 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Paris-DauphineParisFrance
  2. 2.Département, Laboratoire de Mathématiques LMBAUniversité de BrestBrest CedexFrance

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