Many important practical markets inherently involve the interaction of strategic buyers with strategic sellers. A fundamental impossibility result for such two-sided markets due to Myerson and Satterthwaite establishes that even in the simplest such market, that of bilateral trade, it is impossible to design a mechanism that is individually rational, truthful, (weakly) budget balanced, and efficient. Even worse, it is known that the "second best" mechanism-the mechanism that maximizes social welfare subject to the other constraints-has to be carefully tailored to the Bayesian priors and is extremely complex. In light of this impossibility result it is very natural to seek "simple" mechanisms that are approximately optimal, and indeed a very active line of recent work has established a broad spectrum of constant-factor approximation guarantees, which apply to settings well beyond those for which (implicit) characterizations of the optimal (second best) mechanism are known. In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design near-optimal mechanisms with provable, constant-factor approximation guarantees with just a{\em   single sample from the priors! In fact, most of our results in addition to requiring less information also improve upon the best known approximation guarantees for the respective setting .
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors . In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one{\em single sample (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information .
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Many important practical markets inherently involve the interaction of strategic buyers with strategic sellers. A fundamental impossibility result for such two-sided markets due to
A celebrated impossibility result by
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establishes that even in the simplest such market, that of bilateral trade, it is impossible to design a mechanism that is individually rational, truthful, (weakly) budget balanced, and efficient. Even worse, it is known that the "second best" mechanism-the mechanism
(1983) shows that any truthful mechanism for two-sided markets
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subject to
must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of
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other constraints-has to be carefully tailored to the
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and is extremely complex. In light of this impossibility result it is very natural to seek "simple" mechanisms that are approximately optimal, and indeed a very active line of recent work has established a broad spectrum of constant-factor approximation guarantees, which apply to settings well beyond those for which (implicit) characterizations of the optimal (second best) mechanism are known. In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design
. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with
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mechanisms with provable, constant-factor approximation guarantees with just a
approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one
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single sample
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(one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one
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the priors! In fact, most of our results in addition to requiring less information also improve upon the best known approximation guarantees for the respective setting
each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information