TY - JOUR
T1 - Semi-cooperative strategies for differential games
JF - Internat. J. Game Theory 32 (2004) 561-593
Y1 - 2004
A1 - Alberto Bressan
A1 - Wen Shen
AB - The 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.
PB - Springer
UR - http://hdl.handle.net/1963/2893
U1 - 1807
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -