Cycles and collusion in congestion games under Q-learning

TL;DR

This paper analyzes how Q-learning dynamics in network routing games can lead to cycles or convergence to Nash equilibria, revealing challenges in regulation and collusion in such systems.

Contribution

It provides a comprehensive convergence analysis of Q-learning in generalized Braess paradox games, highlighting phenomena like cycling and the impact of meta-game incentives.

Findings

Q-learning can lead to cycling or convergence in routing games.

Meta-game incentives influence agent parameters and outcomes.

Results have implications for regulation and collusion in network games.

Abstract

We investigate the dynamics of Q-learning in a class of generalized Braess paradox games. These games represent an important class of network routing games where the associated stage-game Nash equilibria do not constitute social optima. We provide a full convergence analysis of Q-learning with varying parameters and learning rates. A wide range of phenomena emerges, broadly either settling into Nash or cycling continuously in ways reminiscent of "Edgeworth cycles" (i.e. jumping suddenly from Nash toward social optimum and then deteriorating gradually back to Nash). Our results reveal an important incentive incompatibility when thinking in terms of a meta-game being played by the designers of the individual Q-learners who set their agents' parameters. Indeed, Nash equilibria of the meta-game are characterized by heterogeneous parameters, and resulting outcomes achieve little to no cooperation beyond Nash. In conclusion, we suggest a novel perspective for thinking about regulation and collusion, and discuss the implications of our results for Bertrand oligopoly pricing games.