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

**Full text of the article:**

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