Slicing the Nash equilibrium manifold

Levy, Y. J. (2023) Slicing the Nash equilibrium manifold. Journal of Fixed Point Theory and Applications, 25(4), 85. (doi: 10.1007/s11784-023-01088-2)

Abstract

This paper uses tools on the structure of the Nash equilibrium correspondence of strategic-form games to characterize a class of fixed-point correspondences, that is, correspondences assigning, for a given parametrized function, the fixed-points associated with each value of the parameter. After generalizing recent results from the game-theoretic literature, we deduce that every fixed-point correspondence associated with a semi-algebraic function is the projection of a Nash equilibrium correspondence, and hence its graph is a slice of a projection, as well as a projection of a slice, of a manifold that is homeomorphic, even isotopic, to a Euclidean space. As a result, we derive an illustrative proof of Browder’s theorem for fixed-point correspondences.

• Item Type: Articles
• Keywords: Nash Equilibrium, structure theorem, semi-algebraic geometry, Browder’s Theorem.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Levy, Dr John
• Authors: Levy, Y. J.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Journal of Fixed Point Theory and Applications
• Publisher: Springer
• ISSN: 1661-7738
• ISSN (Online): 1661-7746
• Copyright Holders: Copyright © The Author(s) 2023
• First Published: First published in Journal of Fixed Point Theory and Applications 25(4):85
• Publisher Policy: Reproduced under a Creative Commons licence