Semi-cooperative strategies for differential games

被引:24
|
作者
Bressan, A [1 ]
Shen, W
机构
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] SISSA, I-34014 Trieste, Italy
关键词
ill-posedness of elliptic Cauchy problems; semi-cooperation; Pareto optimum; weak hyperbolicity;
D O I
10.1007/s001820400180
中图分类号
F [经济];
学科分类号
02 ;
摘要
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.
引用
收藏
页码:561 / 593
页数:33
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