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Strategy-proofness in private good economies with linear preferences: An impossibility result

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  • Cho, Wonki Jo
  • Thomson, William

Abstract

We consider the problem of allocating a social endowment of private goods among a group of n agents with linear preferences. We search for rules that satisfy three standard requirements. First is (Pareto-)efficiency. Second is the fairness requirement of “equal treatment of equals” (in welfare terms). Third is the incentive requirement of “strategy-proofness”: no agent should ever benefit from misrepresenting their preferences. We show that no such rule exists. A variety of domains have been explored and similar negative results have been proved but one would have hoped that the domain of linear preferences is sufficiently narrow to allow for some positive results. Our result dashes such hopes.

Suggested Citation

  • Cho, Wonki Jo & Thomson, William, 2023. "Strategy-proofness in private good economies with linear preferences: An impossibility result," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1012-1017.
    • Handle: RePEc:eee:gamebe:v:142:y:2023:i:c:p:1012-1017
    DOI: 10.1016/j.geb.2023.10.010
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    References listed on IDEAS

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    1. Zhou, Lin, 1990. "On a conjecture by gale about one-sided matching problems," Journal of Economic Theory, Elsevier, vol. 52(1), pages 123-135, October.
    2. Takeshi Momi, 2013. "Note on social choice allocation in exchange economies with Cobb–Douglas preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 787-792, March.
    3. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    4. Kazuhiko Hashimoto, 2008. "Strategy-proofness versus efficiency on the Cobb-Douglas domain of exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 457-473, October.
    5. Jin Li & Jingyi Xue, 2013. "Egalitarian division under Leontief Preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 597-622, November.
    6. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Mackenzie, Andrew & Komornik, Vilmos, 2023. "Fairly taking turns," Games and Economic Behavior, Elsevier, vol. 142(C), pages 743-764.

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    More about this item

    Keywords

    Linear preferences; Efficiency; Equal treatment of equals; Strategy-proofness; Impossibility;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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