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Optimal Robust Mechanism in Bilateral Trading

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  • Komal Malik

Abstract

We consider a model of bilateral trade with private values. The value of the buyer and the cost of the seller are jointly distributed. The true joint distribution is unknown to the designer, however, the marginal distributions of the value and the cost are known to the designer. The designer wants to find a trading mechanism that is robustly Bayesian incentive compatible, robustly individually rational, budget-balanced and maximizes the expected gains from trade over all such mechanisms. We refer to such a mechanism as an optimal robust mechanism. We establish equivalence between Bayesian incentive compatible mechanisms (BIC) and dominant strategy mechanisms (DSIC). We characterise the worst distribution for a given mechanism and use this characterisation to find an optimal robust mechanism. We show that there is an optimal robust mechanism that is deterministic (posted-price), dominant strategy incentive compatible, and ex-post individually rational. We also derive an explicit expression of the posted-price of such an optimal robust mechanism. We also show the equivalence between the efficiency gains from the optimal robust mechanism (max-min problem) and guaranteed efficiency gains if the designer could choose the mechanism after observing the true joint distribution (min-max problem).

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  • Komal Malik, 2022. "Optimal Robust Mechanism in Bilateral Trading," Papers 2212.14367, arXiv.org.
    • Handle: RePEc:arx:papers:2212.14367
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    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2017. "First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue," Econometrica, Econometric Society, vol. 85, pages 107-143, January.
    2. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    3. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    4. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    5. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    6. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
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