2021/11/15 by Moshe Babaioff, Shahar Dobzinski, Babaioff, Moshe +3 · 1 citation
Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Merger and Competition Analysis
paper · pdf · doi:10.48550/arxiv.2111.07790
openalex publication_date 2021/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the classic bilateral trade setting. Myerson and Satterthwaite show that there is no Bayesian incentive compatible and budget-balanced mechanism that obtains the gains from trade of the first-best mechanism. Consider the random-offerer mechanism: with probability (1)/(2) run the seller-offering mechanism, in which the seller offers the buyer a take-it-or-leave-it price that maximizes the expected profit of the seller, and with probability (1)/(2) run the buyer-offering mechanism. Very recently, Deng, Mao, Sivan, and Wang showed that the gains from trade of the random-offerer mechanism is at least a constant factor of \frac 1 8.23≈ 0.121 of the gains from trade of the first best mechanism. Perhaps a natural conjecture is that the gains-from-trade of the random-offerer mechanism, which is known to be at least half of the gains-from-trade of the second-best mechanism, is also at least half of the gains-from-trade of the first-best mechanism. However, in this note we exhibit distributions such as the gains-from trade of the random-offerer mechanism is smaller than a 0.495-fraction of the gains-from-trade of the first-best mechanism.