Stability Analysis of Nash Equilibrium for 2-Agent Loss-Aversion-Based Noncooperative Switched Systems

TL;DR

This paper analyzes the stability of Nash equilibria in two-agent loss-aversion-based noncooperative switched systems with quadratic payoffs, providing conditions for convergence and characterizing switching phenomena.

Contribution

It introduces a stability analysis framework for loss-aversion-based noncooperative switched systems, including conditions for convergence and the concept of flash switching instants.

Findings

Derived sufficient conditions for convergence to Nash equilibrium.

Characterized mode transition sequences and flash switching instants.

Validated results with numerical examples.

Abstract

The stability property of the loss-aversion-based noncooperative switched systems with quadratic payoffs is investigated. In this system, each agent adopts the lower sensitivity parameter in the myopic pseudo-gradient dynamics for the case of losing utility than gaining utility, and both systems' dynamics and switching events (conditions) are depending on agents' payoff functions. Sufficient conditions under which agents' state converges towards the Nash equilibrium are derived in accordance with the location of the Nash equilibrium. In the analysis, the mode transition sequence and interesting phenomena which we call flash switching instants are characterized. Finally, we present several numerical examples to illustrate the properties of our results.