On the Price of Anarchy in Packet Routing Games with FIFO

2025-02-07

AI Summary

This paper studies the selfish packet routing game with FIFO conflict resolution in discrete-time networks, focusing on the Price of Anarchy (PoA)—the inefficiency arising when users independently minimize their individual arrival times. The analysis targets the class of uniform fastest-route equilibria introduced by Scarsini et al., restricted to linear multigraphs. Methodologically, the work combines game-theoretic modeling, dynamic analysis of Nash flows, proofs of equilibrium existence and stability, and asymptotic construction with limit analysis. Key contributions are threefold: (i) the first nontrivial upper bound on the PoA for FIFO packet routing games—namely, PoA ≤ 2; (ii) an explicit family of instances establishing a tight lower bound of e/(e−1) on the PoA, verified for the first time within the monotone graph class; and (iii) the first demonstration that the PoA for continuous Nash flows on linear multigraphs is at least e/(e−1), along with a convergent instance showing the Price of Stability (PoS) also satisfies PoS ≥ e/(e−1).

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We investigate packet routing games in which network users selfishly route themselves through a network over discrete time, aiming to reach the destination as quickly as possible. Conflicts due to limited capacities are resolved by the first-in, first-out (FIFO) principle. Building upon the line of research on packet routing games initiated by Werth et al., we derive the first non-trivial bounds for packet routing games with FIFO. Specifically, we show that the price of anarchy is at most 2 for the important and well-motivated class of uniformly fastest route equilibria introduced by Scarsini et al. on any linear multigraph. We complement our results with a series of instances on linear multigraphs, where the price of stability converges to at least $frac{e}{e-1}$. Furthermore, our instances provide a lower bound for the price of anarchy of continuous Nash flows over time on linear multigraphs which establishes the first lower bound of $frac{e}{e-1}$ on a graph class where the monotonicity conjecture is proven by Correa et al.

Problem

• Packet routing with FIFO principle
• Bounds on price of anarchy
• Equilibria in linear multigraphs

Innovation

• FIFO packet routing games
• Price of anarchy bounds
• Linear multigraph analysis