# Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

## TL;DR

This paper demonstrates that simple, prior-independent mechanisms like Buyer Trade Reduction can achieve welfare levels comparable to optimal mechanisms in two-sided markets by adding just one extra buyer or seller, under certain distributional assumptions.

## Contribution

It introduces Bulow-Klemperer-style results for welfare maximization in two-sided markets, showing how adding a single participant can match optimal welfare without complex prior-dependent mechanisms.

## Key findings

- BTR with one additional buyer matches optimal welfare in i.i.d. settings.
- Bounds on the number of buyers needed for welfare guarantees in different distributions.
- Results extend to adding sellers and include new sampling-based welfare maximization insights.

## Abstract

We consider the problem of welfare maximization in two-sided markets using simple mechanisms that are prior-independent. The Myerson-Satterthwaite impossibility theorem shows that even for bilateral trade, there is no feasible (IR, truthful, 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. We present Bulow-Klemperer-style results to circumvent these hurdles in double-auction markets. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, deterministic, truthful, prior-independent, anonymous). First, in the setting where 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 buyers' values are sampled from one distribution and sellers' from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers'. We present bounds on the number of buyers that, when added, guarantees that BTR in the augmented market have welfare at least as high as the optimal in the original market. Our lower bounds extend to a large class of mechanisms, and all of our results extend to adding sellers instead of buyers. 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.