01056nas a2200121 4500008004300000245005500043210005400098260001300152520069800165100002100863700001400884856003600898 2004 en_Ud 00aSemi-cooperative strategies for differential games0 aSemicooperative strategies for differential games bSpringer3 aThe paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/289300818nas a2200121 4500008004300000245007100043210006900114260000900183520043300192100002100625700001400646856003600660 2004 en_Ud 00aSmall BV solutions of hyperbolic noncooperative differential games0 aSmall BV solutions of hyperbolic noncooperative differential gam bSIAM3 aThe paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/2917