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