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Vickrey allocation rule with income effect

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  • Hiroki Saitoh

    ()

  • Shigehiro Serizawa

    ()

Abstract

We consider situations where a society tries to efficiently allocate several homogeneous and indivisible goods among agents. Each agent receives at most one unit of the good. For example, suppose that a government wishes to allocate a fixed number of licenses to operate in its country to private companies with highest abilities to utilize the licenses. Usually companies with higher abilities can make more profits by licenses and are willing to pay higher prices for them. Thus, auction mechanisms are often employed to extract the information on companies' abilities and to allocate licenses efficiently. However, if prices are too high, they may damage companies' abilities to operate. Generally high prices may change the benefits agents obtain from the goods unless agents' preferences are quasi-linear, and we call it "income effect". In this paper, we establish that on domains including nonquasi-linear preferences, that is, preferences exhibiting income effect, an allocation rule which satisfies Pareto-efficiency, strategy-proofness, individual rationality, and nonnegative payment uniquely exists and it is the Vickrey allocation rule.
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Suggested Citation

  • Hiroki Saitoh & Shigehiro Serizawa, 2008. "Vickrey allocation rule with income effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 391-401, May.
  • Handle: RePEc:spr:joecth:v:35:y:2008:i:2:p:391-401 DOI: 10.1007/s00199-007-0235-6
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    References listed on IDEAS

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    Cited by:

    1. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    2. Baisa, Brian, 2017. "Auction design without quasilinear preferences," Theoretical Economics, Econometric Society, vol. 12(1), January.
    3. Horioka, Charles Yuji & Gahramanov, Emin & Hayat, Aziz & Tang, Xueli, 2016. "Why Do Children Take Care of Their Elderly Parents? Are the Japanese Any Different?," AGI Working Paper Series 2016-11, Asian Growth Research Institute.
    4. Kazuhiko Hashimoto & Hiroki Saitoh, 2010. "Domain expansion of the pivotal mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 455-470, March.
    5. Shigehiro Serizawa, 2006. "Strategy-Proof and Anonymous Allocation Rules of Indivisible Goods: A New Characterization of Vickrey Allocation Rule," ISER Discussion Paper 0648, Institute of Social and Economic Research, Osaka University.
    6. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 227-245.
    7. Tomoya Kazumura & Shigehiro Serizawa, 2016. "Efficiency and strategy-proofness in object assignment problems with multi-demand preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 633-663, October.
    8. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    9. Baisa, Brian, 2016. "Overbidding and inefficiencies in multi-unit Vickrey auctions for normal goods," Games and Economic Behavior, Elsevier, vol. 99(C), pages 23-35.
    10. Yuji Fujinaka & Takuma Wakayama, 2008. "Secure Implementation in Shapley-Scarf Housing Markets," ISER Discussion Paper 0727, Institute of Social and Economic Research, Osaka University, revised Feb 2009.
    11. Itai Ashlagi & Shigehiro Serizawa, 2012. "Characterizing Vickrey allocation rule by anonymity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 531-542, March.
    12. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 227-245.
    13. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 147-169.
    14. Toyotaka Sakai, 2012. "Fair waste pricing: an axiomatic analysis to the NIMBY problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 499-521.
    15. repec:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0001-9 is not listed on IDEAS
    16. Tsuyoshi Adachi, 2014. "Equity and the Vickrey allocation rule on general preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 813-830, April.
    17. Nanyang Bu, 2016. "Joint misrepresentation with bribes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 115-125.
    18. Toyotaka Sakai, 2008. "Second price auctions on general preference domains: two characterizations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 347-356.
    19. Mukherjee, Conan, 2015. "On Axioms Underlying Use of Reserve Price," Working Papers 2015:7, Lund University, Department of Economics, revised 14 Apr 2015.
    20. Toyotaka Sakai, 2013. "Axiomatizations of second price auctions with a reserve price," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 255-265, September.

    More about this item

    Keywords

    Strategy-proofness; Allocation rule; Vickrey auction; Income effect; D71; D61; C78; D82;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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