Approximating gains-from-trade in bilateral trading

We consider the design of platforms that facilitate trade between a single seller and a single buyer. The most efficient mechanisms for such settings are complex and sometimes even intractable, and we therefore aim to design simple mechanisms that perform approximately well. We devise a mechanism that always guarantees at least 1/e of the optimal expected gain-from-trade for every set of distributions (assuming monotone hazard rate of the buyer’s distribution). Our main mechanism is extremely simple, and achieves this approximation in Bayes-Nash equilibrium. Moreover, our mechanism approximates the optimal gain-from-trade, which is a strictly harder task than approximating efficiency. Our main impossibility result shows that no Bayes-Nash incentive compatible mechanism can achieve better approximation than 2/e to the optimal gain from trade. We also bound the power of Bayes- Nash incentive compatible mechanisms for approximating the expected efficiency.