Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 21, No. 2, pp. 107-112 (2005)

A generalized Amman's fixed point theorem and its application to Nash equlibrium

Abdelkader Stouti

University Cadi Ayyad

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

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