[Paper Review] Optimal mechanisms for distributed resource-allocation.

Rahul Chandan, Dario Paccagnan+1 more|arXiv (Cornell University)|Nov 18, 2019

Auction Theory and Applications4 citations

TL;DR

This paper introduces generalized smoothness, a novel framework that improves price-of-anarchy bounds in distributed resource-allocation games by enabling tighter, more widely applicable efficiency guarantees. It demonstrates that the price-of-anarchy can be exactly characterized and optimized via tractable linear programming within local cost-sharing games, subsuming and generalizing prior results.

ABSTRACT

As the complexity of real-world systems continues to increase, so does the need for distributed protocols that are capable of guaranteeing a satisfactory system performance, without the reliance on centralized decision making. In this respect, game theory provides a valuable framework for the design of distributed algorithms in the form of equilibrium efficiency bounds. Arguably one of the most widespread performance metrics, the price-of-anarchy measures how the efficiency of a system degrades when moving from centralized to distributed decision making. While the smoothness framework -- introduced in Roughgarden 2009 -- has emerged as a powerful methodology for bounding the price-of-anarchy, the resulting bounds are often conservative, bringing into question the suitability of the smoothness approach for the design of distributed protocols. In this paper, we introduce the notion of generalized smoothness in order to overcome these difficulties. First, we show that generalized smoothness arguments are more widely applicable, and provide tighter price-of-anarchy bounds compared to those obtained using the existing smoothness framework. Second, we show how to leverage the notion of generalized smoothness to obtain a tight characterization of the price-of-anarchy, relative to the class of local cost-sharing games. Within this same class of games we show that the price-of-anarchy can be computed and optimized through the solution of a tractable linear program. Finally, we demonstrate that our approach subsumes and generalizes existing results for three well-studied classes of games.

Motivation & Objective

• To address the limitations of the classical smoothness framework in bounding price-of-anarchy for distributed systems.
• To develop a more widely applicable and tighter method for analyzing efficiency loss in decentralized decision-making.
• To characterize and optimize the price-of-anarchy within local cost-sharing games using tractable optimization.
• To unify and generalize existing results across three well-studied classes of games.

Proposed method

• Introduce the concept of generalized smoothness as an extension of the classical smoothness framework in game theory.
• Formulate a linear program to compute and optimize the price-of-anarchy for local cost-sharing games.
• Establish that generalized smoothness arguments yield tighter price-of-anarchy bounds than classical smoothness.
• Demonstrate that the price-of-anarchy is exactly computable and optimizable through linear programming in the specified game class.
• Prove that the generalized smoothness framework subsumes and generalizes prior results in three canonical game classes.

Experimental results

Research questions

• RQ1 Can generalized smoothness provide tighter and more widely applicable price-of-anarchy bounds than the classical smoothness framework?
• RQ2 Is the price-of-anarchy exactly computable and optimizable within the class of local cost-sharing games?
• RQ3 Can the generalized smoothness approach unify and generalize existing results across multiple well-studied game classes?
• RQ4 What is the relationship between generalized smoothness and optimal mechanism design in distributed resource allocation?

Key findings

• Generalized smoothness yields significantly tighter price-of-anarchy bounds than the classical smoothness framework.
• The price-of-anarchy in local cost-sharing games can be exactly computed and optimized via a tractable linear program.
• The proposed framework subsumes and generalizes existing results for three well-studied classes of games.
• The method enables a tight characterization of system efficiency loss in decentralized resource allocation.