Multivalued Homotopy on an Ordered Set, Fixed and Coincidence Points of Mappings, and Applications in Game Theory


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Abstract

The article develops results of the authors’ previous papers on the topic. The notion of the homotopy of a multivalued mapping of an ordered set is introduced. We study the problem as to whether the existence of a fixed point (or a coincidence point) is preserved under multivalued homotopies of a multivalued mapping (or a pair of multivalued mappings). An application of some of the authors’ previous results on fixed points in game theory is considered.

About the authors

D. A. Podoprikhin

Lomonosov Moscow State University

Author for correspondence.
Email: podoprikhindmitry@gmail.com
Russian Federation, Moscow, 119991

T. N. Fomenko

Lomonosov Moscow State University

Author for correspondence.
Email: tn-fomenko@yandex.ru
Russian Federation, Moscow, 119991

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