On Robustness Properties in Empirical Centroid Fictitious Play

TL;DR

This paper demonstrates that Empirical Centroid Fictitious Play (ECFP) maintains robustness properties similar to classical Fictitious Play, supporting its practical modifications for large-scale game implementations.

Contribution

The paper proves that ECFP retains robustness to step size and response perturbations, enabling practical enhancements akin to those in classical FP.

Findings

ECFP is robust to empirical distribution step size changes.

ECFP maintains stability under best-response perturbations.

Supports practical modifications for large-scale game algorithms.

Abstract

Empirical Centroid Fictitious Play (ECFP) is a generalization of the well-known Fictitious Play (FP) algorithm designed for implementation in large-scale games. In ECFP, the set of players is subdivided into equivalence classes with players in the same class possessing similar properties. Players choose a next-stage action by tracking and responding to aggregate statistics related to each equivalence class. This setup alleviates the difficult task of tracking and responding to the statistical behavior of every individual player, as is the case in traditional FP. Aside from ECFP, many useful modifications have been proposed to classical FP, e.g., rules allowing for network-based implementation, increased computational efficiency, and stronger forms of learning. Such modifications tend to be of great practical value; however, their effectiveness relies heavily on two fundamental properties of FP: robustness to alterations in the empirical distribution step size process, and robustness to best-response perturbations. The main contribution of the paper is to show that similar robustness properties also hold for the ECFP algorithm. This result serves as a first step in enabling practical modifications to ECFP, similar to those already developed for FP.