Semi-cooperative strategies for differential games
The paper contributes to the theory of noncooperative differential games with two players and their Nash equilibrium in feedback form. The main goal of the paper is to manage the fact that the concept of Nash equilibrium is not appropriate for the investigation of such model. The suggested solution is based on the conclusion to allow some degree of cooperative behavior, called semi-cooperation, between players. It is shown that if the semi-cooperative strategies are admitted, then the system of partial differential equations for the value functions turns to be hyperbolic, at least in the weak sense, and the most significant instabilities among Nash equilibrium solutions are removed.
Ill-posedness of elliptic Cauchy problems
scientific article; zbMATH DE number 2143823