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Strategy-proofness and efficiency for non-quasi-linear and common-tiered-object preferences: Characterization of minimum price rule

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  • Zhou, Yu
  • Serizawa, Shigehiro

Abstract

We consider how to assign heterogenous objects to agents and determine their payments. Each agent receives at most one object and has non-quasi-linear preferences over bundles, each consisting of an object and a payment. We focus on the following cases: (i) objects are linearly ranked, and if objects are equally priced, agents prefer a higher-ranked object to a lower-ranked object, or (ii) objects are partitioned into several tiers, and if objects are equally priced, agents prefer an object in the higher tier to an object in the lower tier. First, we analyze the (Walrasian) equilibrium structures in those cases. A minimum price rule assigns a minimum price equilibrium to each preference profile. Second, on the normal-rich common-object-ranking domains and normal-rich common-tiered-object domains, by assuming some conditions, we characterize minimum price rules in terms of agents' welfare, and by four properties, i.e., efficiency, strategy-proofness, individual rationality, and no subsidy.

Suggested Citation

  • Zhou, Yu & Serizawa, Shigehiro, 2018. "Strategy-proofness and efficiency for non-quasi-linear and common-tiered-object preferences: Characterization of minimum price rule," Games and Economic Behavior, Elsevier, vol. 109(C), pages 327-363.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:327-363
    DOI: 10.1016/j.geb.2017.12.019
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    Cited by:

    1. Ryosuke Sakai & Shigehiro Serizawa, 2023. "Strategy-proof mechanism design with non-quasi-linear preferences: ex-post revenue maximization for an arbitrary number of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 103-120, January.
    2. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    3. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    4. Yu Zhou & Shigehiro Serizawa, 2019. "Minimum price equilibrium in the assignment market," ISER Discussion Paper 1047, Institute of Social and Economic Research, Osaka University.
    5. Tomoya KAZUMURA, 2020. "When can we design efficient and strategy-proof rules in package assignment problems?," Discussion papers e-21-008, Graduate School of Economics , Kyoto University.
    6. Komal Malik & Debasis Mishra, 2018. "Pareto efficient combinatorial auctions: dichotomous preferences without quasilinearity," Discussion Papers 18-06, Indian Statistical Institute, Delhi.
    7. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    8. Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    9. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Ryosuke Sakai & Shigehiro Serizawa, 2020. "Strategy-proof mechanism design with non-quasilinear preferences: Ex-post revenue maximization for an arbitrary number of objects," ISER Discussion Paper 1107, Institute of Social and Economic Research, Osaka University.

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    More about this item

    Keywords

    Efficiency; Strategy-proofness; Non-quasi-linearity; Minimum price rule; Equilibrium structure; Normal-richness; Common-object-ranking domain; Common-tiered-object domain;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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