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An Equilibrium Analysis of Knaster’s Fair Division Procedure

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  • Matt Van Essen

    (Department of Economics, Finance, and Legal Studies, University of Alabama, Tuscaloosa, AL 35487, USA)

Abstract

In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, ex-post, the equilibrium allocation is still efficient but may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully— i.e. , the mechanism is ex-ante fair.

Suggested Citation

  • Matt Van Essen, 2013. "An Equilibrium Analysis of Knaster’s Fair Division Procedure," Games, MDPI, vol. 4(1), pages 1-17, January.
    • Handle: RePEc:gam:jgames:v:4:y:2013:i:1:p:21-37:d:22968
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    References listed on IDEAS

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    1. Benny Moldovanu, 2002. "How to Dissolve a Partnership," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 158(1), pages 66-80, March.
    2. Vincent P. Crawford, 1977. "A Game of Fair Division," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 235-247.
    3. Preston McAfee, R., 1992. "Amicable divorce: Dissolving a partnership with simple mechanisms," Journal of Economic Theory, Elsevier, vol. 56(2), pages 266-293, April.
    4. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
    5. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    6. Vincent P. Crawford, 1980. "A Self-administered Solution of the Bargaining Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 385-392.
    7. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
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    Cited by:

    1. Brown, Alexander L. & Van Essen, Matt, 2022. "Breaking-up should not be hard to do! Designing contracts to avoid wars of attrition," European Economic Review, Elsevier, vol. 143(C).

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    Keywords

    fair division; auction;

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