On differential games with long-time-average cost. (English) Zbl 1188.49030

Bardi, Martino

Bernhard, Pierre (ed.) et al., Advances in dynamic games and their applications. Analytical and numerical developments. Selected papers based on the presentations at the 12th international symposium on dynamic games (ISDG) and applications, Sophia Antipolis, France, July 3–6, 2006. Boston, MA: Birkhäuser (ISBN 978-0-8176-4833-6/hbk; 978-0-8176-4834-3/ebook). Annals of the International Society of Dynamic Games 10, 3-18 (2009).

Summary: The paper deals with the ergodicity of deterministic zero-sum differential games with long-time-average cost. Some new sufficient conditions are given, as well as a class of games that are not ergodic. In particular, we settle the issue of ergodicity for the simple games whose associated Isaacs equation is a convex-concave eikonal equation.
For the entire collection see [Zbl 1175.91011].

MSC:

49N70	Differential games and control
37A99	Ergodic theory
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
91A23	Differential games (aspects of game theory)

Keywords:

ergodic control; differential games; viscosity solutions; Hamilton-Jacobi-Isaacs equations