Abstract
A fundamental question in algorithmic mechanism design is whether any approximation algorithm for a single-parameter social-welfare maximization problem can be turned into a dominant-strategy truthful mechanism for the same problem (while preserving the approximation ratio up to a constant factor). A particularly desirable type of transformations—called black-box transformations—achieve the above goal by only accessing the approximation algorithm as a black box.
A recent work by Chawla, Immorlica and Lucier (STOC 2012) demonstrates (unconditionally) the impossibility of certain restricted classes of black-box transformations—where the tranformation is oblivious to the feasibility constrain of the optimization problem. In this work, we remove these restrictions under standard complexity-theoretic assumptions: Assuming the existence of one-way functions, we show the impossibility of all black-box transformations.
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Pass, R., Seth, K. (2014). On the Impossibility of Black-Box Transformations in Mechanism Design. In: Lavi, R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44803-8_24
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DOI: https://doi.org/10.1007/978-3-662-44803-8_24
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