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

TL;DR

This paper introduces a new approach using small-gain techniques from control theory to analyze the robust stability and uniqueness of Nash equilibria in dynamic economic games, exemplified by a Cournot oligopoly model.

Contribution

It pioneers the application of small-gain methods to establish stability conditions for Nash equilibria in dynamic games with functional difference equations.

Findings

Established conditions for global asymptotic stability of Nash equilibria.

Demonstrated the methodology on a Cournot oligopoly model.

Showed the approach guarantees uniqueness of equilibrium.

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.