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The bilateral trade model in a discrete setting

Author

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  • Flesch, J.

    (Quantitative Economics)

  • Schröder, M.J.W.

    (Quantitative Economics)

  • Vermeulen, A.J.

    (Quantitative Economics)

Abstract

We consider a bilateral trade model in which both players have a finite number of possible valuations. The seller's valuation and the buyer's valuation for the object are private information, but the independent beliefs about these valuations are common knowledge. In this setting, we provide a characterization of the set of interim individually rational-implementable trading rules, analogous to the result of Myerson and Satterthwaite [1983]. Thereafter, we derive necessary conditions for incentive compatible and ex post individually rational direct mechanisms. For the special class of corner mechanisms with discrete uniform beliefs, we characterize the set of ex post individually rational-implementable trading rules. In this context it is also shown that ex post efficiency can only be achieved if the number of different valuations is small. The maximal number of different valuations for which efficiency is still possible depends on the prior probability distribution of valuations.

Suggested Citation

  • Flesch, J. & Schröder, M.J.W. & Vermeulen, A.J., 2013. "The bilateral trade model in a discrete setting," Research Memorandum 025, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013025
    DOI: 10.26481/umagsb.2013025
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    References listed on IDEAS

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    1. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
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    3. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    4. Thomas A. Gresik & Mark A. Satterthwaite, 1983. "The Number of Traders Required to Make a Market Competitive: The Beginnings of a Theory," Discussion Papers 551, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Gresik, Thomas A., 1991. "Ex ante efficient, ex post individually rational trade," Journal of Economic Theory, Elsevier, vol. 53(1), pages 131-145, February.
    6. Matsuo, Toshihide, 1989. "On incentive compatible, individually rational, and ex post efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 49(1), pages 189-194, October.
    7. Gresik, Thomas A., 1991. "Efficient bilateral trade with statistically dependent beliefs," Journal of Economic Theory, Elsevier, vol. 53(1), pages 199-205, February.
    8. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
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    Cited by:

    1. Kamyar Kargar & Halil Ibrahim Bayrak & Mustafa Çelebi Pinar, 2018. "Robust bilateral trade with discrete types," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 367-393, December.

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