[Paper Review] A Stackelberg strategy for routing flow over time

Umang Bhaskar, Lisa Fleischer+1 more|arXiv (Cornell University)|Jan 23, 2011

Game Theory and Applications32 references9 citations

TL;DR

This paper proposes an efficiently computable Stackelberg strategy for routing flow over time in competitive network routing games, modeling user decisions more realistically by tracking flow progression over time. It proves that under this strategy, the competitive equilibrium is within a constant factor of optimal for two natural efficiency measures, significantly improving upon prior models that treat flow as instantaneous.

ABSTRACT

Routing games are used to to understand the impact of individual users' decisions on network efficiency. Most prior work on routing games uses a simplified model of network flow where all flow exists simultaneously, and users care about either their maximum delay or their total delay. Both of these measures are surrogates for measuring how long it takes to get all of a user's traffic through the network. We attempt a more direct study of how competition affects network efficiency by examining routing games in a flow over time model. We give an efficiently computable Stackelberg strategy for this model and show that the competitive equilibrium under this strategy is no worse than a small constant times the optimal, for two natural measures of optimality.

Motivation & Objective

• To address the limitations of traditional routing games that model flow as instantaneous, which fails to capture real-world timing dynamics.
• To study how competition affects network efficiency in a more realistic flow-over-time model where users' decisions impact the timing of flow delivery.
• To design a computationally efficient Stackelberg strategy that guides user routing to improve overall network efficiency.
• To prove that the resulting competitive equilibrium under this strategy is within a constant factor of the optimal solution for two key efficiency measures.

Proposed method

• Formalizes a flow-over-time model where flow is injected over time and progresses through the network with link delays.
• Introduces a Stackelberg strategy in which a central authority commits to a routing policy that influences user behavior.
• Uses a linear programming formulation to compute the optimal Stackelberg strategy efficiently.
• Analyzes equilibrium outcomes under the strategy using two efficiency measures: total completion time and maximum completion time.
• Applies game-theoretic analysis to show that the competitive equilibrium is within a constant factor of the optimal solution.
• Employs techniques from network flow and game theory to bound the price of anarchy in the flow-over-time setting.

Experimental results

Research questions

• RQ1 How does competition in a flow-over-time network model affect overall network efficiency compared to instantaneous flow models?
• RQ2 Can a centralized Stackelberg strategy be computed efficiently to guide user routing and improve system-wide performance?
• RQ3 What is the worst-case performance ratio (price of anarchy) of the competitive equilibrium under such a strategy?
• RQ4 How do different efficiency measures—total completion time and maximum completion time—behave under the Stackelberg strategy?

Key findings

• The proposed Stackelberg strategy can be computed efficiently using linear programming.
• The competitive equilibrium resulting from the strategy is within a constant factor of the optimal solution for both total completion time and maximum completion time.
• The performance guarantee holds regardless of network size or topology, under the given flow-over-time model.
• The analysis establishes a constant upper bound on the price of anarchy, demonstrating robustness of the strategy.