A Network Game of Dynamic Traffic

TL;DR

This paper analyzes a dynamic traffic network game with atomic agents, proving the existence of equilibria, comparing models, and demonstrating properties like Pareto optimality and bounded queue lengths in specific network classes.

Contribution

It introduces a dynamic traffic game model with proven equilibrium existence, compares it to simplified models, and establishes properties and bounds for equilibrium flows in series-parallel networks.

Findings

Existence of subgame perfect equilibrium in the dynamic traffic game.

Nash equilibria are also strong and weakly Pareto optimal.

Queue lengths are bounded in series-parallel networks under certain conditions.

Abstract

We study a network congestion game of discrete-time dynamic traffic of atomic agents with a single origin-destination pair. Any agent freely makes a dynamic decision at each vertex (e.g., road crossing) and traffic is regulated with given priorities on edges (e.g., road segments). We first constructively prove that there always exists a subgame perfect equilibrium (SPE) in this game. We then study the relationship between this model and a simplified model, in which agents select and fix an origin-destination path simultaneously. We show that the set of Nash equilibrium (NE) flows of the simplified model is a proper subset of the set of SPE flows of our main model. We prove that each NE is also a strong NE and hence weakly Pareto optimal. We establish several other nice properties of NE flows, including global First-In-First-Out. Then for two classes of networks, including series-parallel ones, we show that the queue lengths at equilibrium are bounded at any given instance, which means the price of anarchy of any given game instance is bounded, provided that the inflow size never exceeds the network capacity.