
Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders
A longstanding open problem in Algorithmic Mechanism Design is to design...
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Improved Truthful Mechanisms for Subadditive Combinatorial Auctions: Breaking the Logarithmic Barrier
We present a computationallyefficient truthful mechanism for combinator...
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Separating the Communication Complexity of Truthful and NonTruthful Combinatorial Auctions
We provide the first separation in the approximation guarantee achievabl...
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Twoplayer entangled games are NPhard
We show that the maximum success probability of players sharing quantum ...
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In Congestion Games, Taxes Achieve Optimal Approximation
We consider the problem of minimizing social cost in atomic congestion g...
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Aggregated Deletion Propagation for Counting Conjunctive Query Answers
We investigate the computational complexity of minimizing the source sid...
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Learning in Auctions: Regret is Hard, Envy is Easy
A line of recent work provides welfare guarantees of simple combinatoria...
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Implementation in Advised Strategies: Welfare Guarantees from PostedPrice Mechanisms when Demand Queries are NPhard
Stateoftheart postedprice mechanisms for submodular bidders with m items achieve approximation guarantees of O((loglog m)^3) [Assadi and Singla, 2019]. Their truthfulness, however, requires bidders to compute an NPhard demandquery. Some computational complexity of this form is unavoidable, as it is NPhard for truthful mechanisms to guarantee even an m^1/2εapproximation for any ε > 0 [Dobzinski and Vondrák, 2016]. Together, these establish a stark distinction between computationallyefficient and communicationefficient 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 polytime mechanism guarantees an αapproximation in implementation in advised strategies if there exists polytime advice for each player such that an αapproximation is achieved whenever all players follow advice. Using an appropriate bicriterion notion of approximate demand queries (which can be computed in polytime), we establish that (a slight modification of) the [Assadi and Singla, 2019] mechanism achieves the same O((loglog m)^3)approximation in implementation in advised strategies.
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