Geodesic
Nash equilibrium in differential games and the construction of the programmed iteration method
Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 621-647

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This work is devoted to the study of nonzero-sum differential games. The set of payoffs in a situation of Nash equilibrium is examined. It is shown that the set of payoffs in a situation of Nash equilibrium coincides with the set of values of consistent functions which are fixed points of the program absorption operator. A condition for functions to be consistent is given in terms of the weak invariance of the graph of the functions under a certain differential inclusion. Bibliography: 18 titles.
Keywords: differential games, Nash equilibrium, programmed iteration method. 
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Yu. V. Averboukh. Nash equilibrium in differential games and the construction of the programmed iteration method. Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 621-647. http://geodesic.mathdoc.fr/item/SM_2011_202_5_a0/