Strategy-Proof Approximations of Optimal E iciency in Bilateral Trade

We consider strategy-proof mechanisms for the bilateral trade problem studied originally by Cha‹erjee and Samuelson [1983] and Myerson and Sa‹erthwaite [1983], in which a seller and a buyer bargain over a single indivisible good. First, we show that there exists a €xed-price mechanism that achieves at least a (1 − 1/e + 0.0001)-fraction of the optimal eciency, thus improving the previous (1 − 1/e)-approximation Blumrosen and Dobzinski [2016]. We also improve the known hardness bound, showing that no €xed-price mechanism can achieve a factor be‹er than 0.7385. Second, we solve completely a special case of the problem in which both seller and buyer have identical distributions. We show that in this case the optimal approximation factor for €xed-price mechanisms is exactly 2+ √ 2 4 ' 0.8536.