Distributed Prediction-Correction Algorithms for Time-Varying Nash Equilibrium Tracking

TL;DR

This paper introduces a distributed prediction-correction algorithm for tracking time-varying Nash equilibria in dynamic environments, demonstrating bounded tracking error and convergence properties through theoretical analysis and simulations.

Contribution

The paper proposes a novel distributed prediction-correction algorithm (DPCA) that effectively tracks time-varying Nash equilibria with bounded error and linear convergence in static cases.

Findings

The algorithm achieves bounded tracking error for time-varying NE.

Tracking error can be minimized with smaller sampling periods.

Numerical simulations confirm effective NE tracking in multi-robot scenarios.

Abstract

This paper focuses on a time-varying Nash equilibrium trajectory tracking problem, that is applicable to a wide range of non-cooperative game applications arising in dynamic environments. To solve this problem, we propose a distributed prediction correction algorithm, termed DPCA, in which each player predicts future strategies based on previous observations and then exploits predictions to effectively track the NE trajectory by using one or multiple distributed gradient descent steps across a network. We rigorously demonstrate that the tracking sequence produced by the proposed algorithm is able to track the time-varying NE with a bounded error. We also show that the tracking error can be arbitrarily close to zero when the sampling period is small enough. Furthermore, we achieve linear convergence for the time-invariant Nash equilibrium seeking problem as a special case of our results. Finally, a numerical simulation of a multi-robot surveillance scenario verifies the tracking performance and the prediction necessary for the proposed algorithm.