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|Abstract:||State-of-the-art posted-price mechanisms for submodular bidders with m items achieve approximation guarantees of O((log log m)^3) [Sepehr Assadi and Sahil Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard demand-query. Some computational complexity of this form is unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an m^(1/2-ε)-approximation for any ε > 0 [Shahar Dobzinski and Jan Vondrák, 2016]. Together, these establish a stark distinction between computationally-efficient and communication-efficient truthful mechanisms. We show that this distinction disappears with a mild relaxation of truthfulness, which we term implementation in advised strategies. Specifically, advice maps a tentative strategy either to that same strategy itself, or one that dominates it. We say that a player follows advice as long as they never play actions which are dominated by advice. A poly-time mechanism guarantees an α-approximation in implementation in advised strategies if there exists advice (which runs in poly-time) for each player such that an α-approximation is achieved whenever all players follow advice. Using an appropriate bicriterion notion of approximate demand queries (which can be computed in poly-time), we establish that (a slight modification of) the [Sepehr Assadi and Sahil Singla, 2019] mechanism achieves the same O((log log m)^3)-approximation in implementation in advised strategies.|
|Citation:||Cai, Linda, Clay Thomas, and S. Matthew Weinberg. "Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard." In 11th Innovations in Theoretical Computer Science Conference (ITCS) (2020): 61:1-61:32. doi:10.4230/LIPIcs.ITCS.2020.61|
|Pages:||61:1 - 61:32|
|Type of Material:||Conference Article|
|Journal/Proceeding Title:||11th Innovations in Theoretical Computer Science Conference|
|Version:||Final published version. This is an open access article.|
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