Carathéodory's method for a class of dynamic games.
The author gives an overview of Carathéodory method and he proves a verification theorem for nonzero sum games. The suppositions of the main theorem (verifications) assume the differentiability of the value functions. Existence results of feedback Nash equilibria (without assuming the differentiability of the values) can be found in [\textit{A. F. Konomenko}, Sov. Math., Dokl. 17, 1557--1560 (1977; Zbl 0366.90141); \textit{A. F. Kleimenof}, Nonantagonistic differential games, Nauk. Ural. Otdelenie, Ekaterinburg (1993)]. At the end two examples of linear quadratic games are discussed.
verification theorem for nonzero sum games
scientific article; zbMATH DE number 1866764
scientific article