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Two-sided allocation problems, decomposability, and the impossibility of efficient trade

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  • Delacrétaz, David
  • Loertscher, Simon
  • Marx, Leslie M.
  • Wilkening, Tom
Abstract
Previous literature has shown that private information is a transaction cost that prevents efficient reallocation in two-sided setups with bilateral trade or homogeneous goods. We derive conditions under which the impossibility of efficient trade extends to rich environments in which buyers and sellers have multi-dimensional private types, accommodating many-to-many trades and heterogeneous objects. If agents can be decomposed into unit constituents, the allocation problem can be represented as an assignment game and impossibility obtains through a generalization of Shapley's (1962) result that buyers and sellers are complements. We introduce a general family of payoff functions that ensures decomposability and thus impossibility.

Suggested Citation

  • Delacrétaz, David & Loertscher, Simon & Marx, Leslie M. & Wilkening, Tom, 2019. "Two-sided allocation problems, decomposability, and the impossibility of efficient trade," Journal of Economic Theory, Elsevier, vol. 179(C), pages 416-454.
    • Handle: RePEc:eee:jetheo:v:179:y:2019:i:c:p:416-454
    DOI: 10.1016/j.jet.2018.11.004
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    Cited by:

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    7. Tobias Widmer & Paul Karaenke & Vijayan Sugumaran, 2021. "Two‐sided service markets: Effects of quality differentiation on market efficiency," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 588-604, April.
    8. Delacrétaz, David & Kominers, Scott Duke & Nichifor, Alexandru, 2020. "Comparative statics for size-dependent discounts in matching markets," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 127-131.
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    More about this item

    Keywords

    Mechanism design; Assignment games; Impossibility theorems; Decomposability; Size-dependent discounts;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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