Abstract.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Revised: May 2004
Rights and permissions
About this article
Cite this article
Bressan, A., Shen, W. Semi-cooperative strategies for differential games. Int J Game Theory 32, 561–593 (2004). https://doi.org/10.1007/s001820400180
Issue Date:
DOI: https://doi.org/10.1007/s001820400180