Distributed Inertial Best-Response Dynamics

TL;DR

This paper introduces distributed inertial best-response dynamics based on fictitious play, demonstrating their robustness and convergence to pure Nash equilibria in networked multi-agent settings through consensus-based algorithms and simulations.

Contribution

It develops fully distributed inertial fictitious play algorithms with convergence guarantees for pure Nash equilibria in networked environments.

Findings

Algorithms converge to pure NE

Robustness to informational limitations

Validated through numerical simulations

Abstract

The note considers the problem of computing pure Nash equilibrium (NE) strategies in distributed (i.e., network-based) settings. The paper studies a class of inertial best response dynamics based on the fictitious play (FP) algorithm. It is shown that inertial best response dynamics are robust to informational limitations common in distributed settings. Fully distributed variants of FP with inertia and joint strategy FP with inertia are developed and convergence is proven to the set of pure NE. The distributed algorithms rely on consensus methods. Results are validated using numerical simulations.