How Bad is Selfish Driving? Bounding the Inefficiency of Equilibria in Urban Driving Games

TL;DR

This paper models urban driving as a general-sum game to analyze the inefficiency of equilibria, providing bounds on the Price of Anarchy that depend on specific game parameters and demonstrating practical relevance with reinforcement learning.

Contribution

It introduces novel bounds on equilibrium inefficiency in urban driving games modeled as congestion games, refining existing theoretical guarantees with problem-specific parameters.

Findings

New bounds on Price of Anarchy as a function of game parameters

Efficient equilibria observed with reinforcement learning policies

Refined theoretical guarantees for congestion-based driving games

Abstract

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most efficient equilibrium (in term of social cost) is often impractical from a computational standpoint, in this work we study the (in)efficiency of any equilibrium players might agree to play. More specifically, we bound the equilibrium inefficiency by modeling driving games as particular type of congestion games over spatio-temporal resources. We obtain novel guarantees that refine existing bounds on the Price of Anarchy (PoA) as a function of problem-dependent game parameters. For instance, the relative trade-off between proximity costs and personal objectives such as comfort and progress. Although the obtained guarantees concern open-loop trajectories, we observe efficient equilibria even when agents employ closed-loop policies trained via decentralized multi-agent reinforcement learning.