Abstract
Black-box transformations have been extensively studied in algorithmic mechanism design as a generic tool for converting algorithms into truthful mechanisms without degrading the approximation guarantees. While such transformations have been designed for a variety of settings, Chawla et al. showed that no fully general black-box transformation exists for single-parameter environments. In this paper, we investigate the potentials and limits of black-box transformations in the prior-free (i.e., non-Bayesian) setting in downward-closed single-parameter environments, a large and important class of environments in mechanism design. On the positive side, we show that such a transformation can preserve a constant fraction of the welfare at every input if the private valuations of the agents take on a constant number of values that are far apart, while on the negative side, we show that this task is not possible for general private valuations.
Highlights
Mechanism design is a science of rule-making
Since downward-closed environments occur in a wide variety of settings in mechanism design, including knapsack auctions and combinatorial auctions, we find the question that we study to be a natural and important one
We show that if a monotone black-box transformation preserves the approximation ratio of any given input algorithm A, on some input v it must query A on an input that has Hamming distance (n) from v
Summary
Mechanism design is a science of rule-making. Its goal is to design rules so that individual strategic behavior of the agents leads to desirable global outcomes. The widespread success of designing computationally tractable mechanisms with optimal approximation guarantees has raised the question of whether there exists a generic method for transforming any computationally tractable algorithm into a computationally tractable mechanism without degrading the approximation guarantee Such a method would not be allowed access to the description of the algorithm but instead would only be able to query the algorithm at specific inputs, and is known as a “black-box transformation”. Since downward-closed environments occur in a wide variety of settings in mechanism design, including knapsack auctions and combinatorial auctions, we find the question that we study to be a natural and important one We consider such settings and assume, crucially, that the black-box transformation is aware that the feasible set is downward-closed. We investigate the potentials and limits of black-box transformations when they are endowed with this extra power
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