Routing Games over Time with FIFO policy

TL;DR

This paper analyzes atomic routing games with FIFO queues, revealing computational hardness for equilibrium existence and best-response optimization, and introduces a GPS-based behavioral model to study efficiency in such dynamic routing scenarios.

Contribution

It demonstrates the computational complexity of equilibrium analysis in FIFO-based routing games and proposes a behavioral model based on GPS navigation for efficiency assessment.

Findings

Best-response optimization is not approximable.

Deciding Nash equilibrium existence is 0complete for the second level of the polynomial hierarchy.

GPS-based behavioral model provides insights into worst-case efficiency ratios.

Abstract

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.