Nash equilibrium and robust stability in dynamic games: A small-gain perspective

Authors:
Iasson Karafyllis;Zhong-Ping Jiang;George Athanasiou
Affiliations:
Department of Environmental Engineering, Technical University of Crete, 73100, Chania, Greece;Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, NY 11201, USA;TT Hellenic Postbank, Financial Services, 2-6 Pesmazoglou str., 101 75, Athens, Greece
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions guaranteeing uniqueness and global asymptotic stability of a Nash equilibrium point for economic models described by functional difference equations. Specification to a Cournot oligopoly game is studied in detail to demonstrate the power of the proposed methodology.