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Improved Approximation to First-Best Gains-from-Trade

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  • Yumou Fei

Abstract

We study the two-agent single-item bilateral trade. Ideally, the trade should happen whenever the buyer's value for the item exceeds the seller's cost. However, the classical result of Myerson and Satterthwaite showed that no mechanism can achieve this without violating one of the Bayesian incentive compatibility, individual rationality and weakly balanced budget conditions. This motivates the study of approximating the trade-whenever-socially-beneficial mechanism, in terms of the expected gains-from-trade. Recently, Deng, Mao, Sivan, and Wang showed that the random-offerer mechanism achieves at least a 1/8.23 approximation. We improve this lower bound to 1/3.15 in this paper. We also determine the exact worst-case approximation ratio of the seller-pricing mechanism assuming the distribution of the buyer's value satisfies the monotone hazard rate property.

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  • Yumou Fei, 2022. "Improved Approximation to First-Best Gains-from-Trade," Papers 2205.00140, arXiv.org.
    • Handle: RePEc:arx:papers:2205.00140
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    References listed on IDEAS

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    1. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    2. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
    3. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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