Existence of open-loop equilibria in differential games with impulsive effects suffered by logic choice

This paper proposes a novel class of differential games where one player adopts piecewise constant strategies and the other implements impulse suffered by logic choice. To the best of our knowledge, the discussion in this paper has been the first try to investigate differential games with impulsive effects suffered by logic choice. Based on semi -tensor product, impulsive effects suffered by logic choice can be represented algebraically. The form of impulse in this paper is more general than those in previous related literature. Further, the existence of open -loop Nash equilibria is investigated and verification conditions are obtained. At last, the case of multiobjects is generalized, and verification theorems about the existence of weakly Pareto-Nash equilibria are derived.