Constrained weak Nash-type equilibrium problems (Q1723818)

Summary: A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. The results extend the corresponding one of \textit{J.-Y. Fu} [J. Math. Anal. Appl. 285, No. 2, 708--713 (2003; Zbl 1031.49013)]. In particular, if the payoff functions are singlevalued, our existence theorem extends the main results of [loc. cit.] by relaxing the assumption of convexity.