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A generalized amman’s fixed point theorem and its application to nash equlibrium.
| Content Provider | CiteSeerX |
|---|---|
| Author | Stouti, Abdelkader |
| Abstract | Abstract. In this paper, we first give a generalization of Amann’s fixed point theorem: if (X,≤) is a nonempty partially ordered set with the property that every nonempty chain has a supremum and F: X → 2X is a monotone set-valued map and there is a ∈ X such that for all b ∈ F (a) we have a ≤ b, then F has a least fixed point in the subset {x ∈ X: a ≤ x}. 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. 1. Introduction and |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Monotone Set-valued Map Fixed Point Nash Equilibrium Duality Principle Point Theorem Supermodular Game Nonempty Chain |
| Content Type | Text |
| Resource Type | Article |
