Calculus of Variations and Geometric Measure Theory

M. Bardi

On differential games with long-time-average cost

created by bardi on 06 Sep 2007
modified on 15 Dec 2009


Published Paper

Inserted: 6 sep 2007
Last Updated: 15 dec 2009

Journal: Ann. Internat. Soc. Dynam. Games
Volume: 10
Pages: 3-18
Year: 2009

" Advances in Dynamic games and their Applications", P. Bernhard, V. Gaitsgory, O. Pourtallier editors


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.

Keywords: Hamilton-Jacobi-Isaacs equations, Ergodic control, differential games