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arXiv · 2211.13113

On Fixed Points of Locally and Pointwise Contractive Set-Valued Maps with an Application to the Existence of Nash Equilibrium in Games

Ted Loch-Temzelides
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Abstract

We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach's contraction property. As an application, we demonstrate the existence of Nash equilibrium in a general class of strategic games played on metric spaces of strategies.

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Ted Loch-Temzelides. 2022-11-23. On Fixed Points of Locally and Pointwise Contractive Set-Valued Maps with an Application to the Existence of Nash Equilibrium in Games. https://doi.org/10.1007/s11784-022-00998

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