Nash equilibrium selection by eigenvalue control

TL;DR

This paper demonstrates how eigenvalue control techniques can be used to influence the selection of Nash equilibria in a game with two equilibria, bridging control theory and game dynamics.

Contribution

It introduces a novel method to control equilibrium selection in game dynamics using pole assignment, a concept from modern control theory.

Findings

Long-term strategy distribution can be controlled by pole assignment.

First theoretical framework for equilibrium control in game dynamics.

Potential for laboratory human subject experiments to verify the approach.

Abstract

People choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. The process can be modelled as an evolutionary game dynamics system, which may be controllable. In modern control theory, eigenvalue (pole) assignment is a basic approach to designing a full-state feedback controller, which can influence the outcome of a game. This study shows that, in a game with two Nash equilibria, the long-running strategy distribution can be controlled by pole assignment. We illustrate a theoretical workflow to design and evaluate the controller. To our knowledge, this is the first realisation of the control of equilibrium selection by design in the game dynamics theory paradigm. We hope the controller can be verified in a laboratory human subject game experiment.