Nash Equilibrium and Robust Stability in Dynamic Games: A Small-Gain Perspective

Karafyllis, Iasson and Jiang, Zhong-Ping and Athanasiou, George (2010): Nash Equilibrium and Robust Stability in Dynamic Games: A Small-Gain Perspective. Published in: Computers and Mathematics with Applications , Vol. 60, No. 11 (1 December 2010): pp. 2936-2952.

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 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic game; Cournot oligopoly; Nash equilibrium; Robust stability; Small gain
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

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