Robustness Properties in Fictitious-Play-Type Algorithms

TL;DR

This paper analyzes the robustness of Fictitious-Play-type algorithms in game-theoretic learning, demonstrating their convergence under realistic conditions like limited information, asynchronous updates, and partial observability in control scenarios.

Contribution

It provides a unified robustness analysis of FP-type algorithms under perturbations, extending convergence guarantees to more realistic decentralized control settings.

Findings

Robustness of FP-type algorithms to perturbations is established.

Convergence results are derived for distributed, asynchronous, and continuous-time implementations.

The analysis broadens the applicability of game-theoretic learning in practical control systems.

Abstract

Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic control scenarios. This paper considers a broad class of best response learning algorithms, that we refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information about the history of actions, each individual forecasts the future play and chooses a (myopic) best action given their forecast. We provide a unifed analysis of the behavior of FP-type algorithms under an important class of perturbations, thus demonstrating robustness to deviations from the idealistic operating conditions that have been previously assumed. This robustness result is then used to derive convergence results for two control-relevant relaxations of standard game-theoretic applications: distributed (network-based) implementation without full observability and asynchronous deployment (including in continuous time). In each case the results follow as a direct consequence of the main robustness result.