Core Concepts
Augmenting a two-sided market with a constant number of additional buyers and sellers can enable a simple, prior-independent mechanism to achieve gains from trade at least as high as the optimal mechanism in the original market.
Abstract
The paper studies the problem of maximizing the gains from trade (GFT) in two-sided markets, where there are m unit-demand buyers and n unit-supply sellers. The authors consider the double auction setting and focus on the GFT as the measure of efficiency.
The key insights are:
Seller Trade Reduction (STR), a variant of the Trade Reduction mechanism, can achieve GFT at least as high as the first-best GFT in the original market by augmenting the market with a constant number of additional buyers and sellers, when the buyers' value distribution first-order stochastically dominates the sellers' distribution.
For any ε > 0 and any set of O(1/ε) buyers and O(1/ε) sellers where the buyers' value exceeds the sellers' value with constant probability, augmenting these agents into any market allows the Trade Reduction mechanism to achieve a (1-ε)-approximation of the optimal GFT in the augmented market, without any knowledge of the original market.
The key technical contributions are:
Constructing carefully designed "good" and "bad" events to analyze the GFT difference between STR and the first-best allocation in the augmented market.
Developing a coupling argument to show that the optimal GFT comes mainly from instances where there are a large number of trades, enabling a constant-factor approximation result.