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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.

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Bibliographic Info

Article provided by MDPI, Open Access Journal in its journal Games.

Volume (Year): 4 (2013)
Issue (Month): 1 (January)
Pages: 21-37

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Handle: RePEc:gam:jgames:v:4:y:2013:i:1:p:21-37:d:22968

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Keywords: fair division; auction;

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  1. Crawford, Vincent P, 1977. "A Game of Fair Division," Review of Economic Studies, Wiley Blackwell, vol. 44(2), pages 235-47, June.
  2. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  3. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
  4. 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.
  5. Preston McAfee, R., 1992. "Amicable divorce: Dissolving a partnership with simple mechanisms," Journal of Economic Theory, Elsevier, vol. 56(2), pages 266-293, April.
  6. Benny Moldovanu, 2002. "How to Dissolve a Partnership," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 158(1), pages 66-, March.
  7. Crawford, Vincent P, 1980. "A Self-administered Solution of the Bargaining Problem," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 385-92, January.
  8. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-39, July.
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