Fast Convergence in Semi-Anonymous Potential Games

TL;DR

This paper introduces a modified log-linear learning algorithm for potential games that achieves near-linear convergence time relative to the number of players, even with dynamic participation.

Contribution

It formalizes a new algorithm with improved convergence guarantees for semi-anonymous potential games, including dynamic player entry and exit.

Findings

Convergence time is roughly linear in the number of players.

The algorithm applies to games with aggregate utility functions.

Performance remains robust with changing player populations.

Abstract

Log-linear learning has been extensively studied in both the game theoretic and distributed control literature. It is appealing for many applications because it often guarantees that the agents' collective behavior will converge in probability to the optimal system configuration. However, the worst case convergence time can be prohibitively long, i.e., exponential in the number of players. We formalize a modified log-linear learning algorithm whose worst case convergence time is roughly linear in the number of players. We prove this characterization for a class of potential games where agents' utility functions can be expressed as a function of aggregate behavior within a finite collection of populations. Finally, we show that the convergence time remains roughly linear in the number of players even when the players are permitted to enter and exit the game over time.