Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets
Kira Goldner and
Yannai A. Gonczarowski
Papers from arXiv.org
We consider the problem of welfare maximization in two-sided markets using simple mechanisms that are prior-independent. The seminal impossibility result of Myerson and Satterthwaite  shows that even for bilateral trade, there is no feasible (IR, truthful and budget balanced) mechanism that has welfare as high as the optimal-yet-infeasible VCG mechanism, which attains maximal welfare but runs a deficit. On the other hand, the optimal feasible mechanism needs to be carefully tailored to the Bayesian prior, and is extremely complex, eluding a precise description. In this paper we present Bulow-Klemperer-style results to circumvent these hurdles in double-auction market settings. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, that is feasible and simple (in particular, it is deterministic, prior-independent, and anonymous). First, in the setting where the buyers' and sellers' values are sampled i.i.d. from the same distribution, we show that for any such market of any size, BTR with one additional buyer whose value is sampled from the same distribution has expected welfare at least as high as the optimal in the original market. We then move to a more general setting where the buyers' values are sampled from one distribution, and the sellers' from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers' distribution. We present bounds on the number of buyers that, when added, cause BTR in the augmented market to achieve welfare at least as high as the optimal in the original market. Our lower bounds extend to a large class of mechanisms. In addition, we present positive results about the usefulness of pricing at a sample for welfare maximization in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context.
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