Optimal mechanisms for distributed resource-allocation
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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.
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