Quasi-Variational Inequalities without the Concavity Assumption

This paper generalizes a foundational quasi-variational inequality by relaxing the (0-diagonal) concavity condition. The approach adopted in this paper is based on continuous selection-type arguments and hence it is quite different from the approach used in the literature. Thus it enables us to prose the existence of equilibrium of the constrained noncooperative games without assuming the (quasi) convexity of loss functions.