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 -
TY - JOUR
T1 - Small BV solutions of hyperbolic noncooperative differential games
JF - SIAM J. Control Optim. 43 (2004) 194-215
Y1 - 2004
A1 - Alberto Bressan
A1 - Wen Shen
AB - The 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.
PB - SIAM
UR - http://hdl.handle.net/1963/2917
U1 - 1783
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -