Abstract: In this paper, we first give a generalization of Amann's fixed point theorem. By using the duality principle, we obtain the existence of the greatest fixed point for monotone set-valued maps. As application we apply our results to show that the set of Nash equilibrium of a subcategory of D'Orey's extended supermodular game has a least and a greatest elements.
Keywords: Fixed points, set-valued map, supermodular game, Nash equilibrium.
Classification (MSC2000): 06B23; 54C60, 47H10
Full text of the article: