Generic Stability of the Weakly Pareto-Nash Equilibrium with Strategy Transformational Barriers

Abstract

The object of this paper is to establish a new model with strategy transformational barriers for a class of generalized multileader multifollower multiple objective games (GMLMFMOG) and further deduce some new results of the weakly Pareto-Nash equilibrium (WPNE) with strategy transformational barriers for the GMLMFMOG. First, we investigate the existence of the WPNE with strategy transformational barriers for the GMLMFMOG by using the Kakutani-Fan-Glicksberg fixed point theory. Next, we study the generic stability of the GMLMFMOG with strategy transformational barriers in Hausdorff space. Finally, we obtain that the majority of the WPNE with strategy transformational barriers for the GMLMFMOG are essential on the meaning of Baire’s category. In addition, we demonstrate that there is at least an essential component for the GMLMFMOG with strategy transformational barriers.