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Efficiency and strategy-proofness in object assignment problems with multi-demand preferences

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  • Tomoya Kazumura

    (Osaka University)

  • Shigehiro Serizawa

    (Osaka University)

Abstract

We consider the problem of allocating sets of objects to agents and collecting payments. Each agent has a preference relation over the set of pairs consisting of a set of objects and a payment. Preferences are not necessarily quasi-linear. Non-quasi-linear preferences describe environments where the wealth effect is non-negligible: the payment level changes agents’ willingness to pay for swapping sets. We investigate the existence of efficient and strategy-proof rules. A preference relation is unit-demand if given a payment level, for each set of objects, the most preferred one in the set is at least as good as the set itself; it is multi-demand if given a payment level, when an agent receives an object, receiving some additional object(s) makes him better off. We show that if a domain contains enough variety of unit-demand preferences and at least one multi-demand preference relation, and if there are more agents than objects, then no rule satisfies efficiency, strategy-proofness, individual rationality, and no subsidy for losers on the domain.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:47:y:2016:i:3:d:10.1007_s00355-016-0986-8
    DOI: 10.1007/s00355-016-0986-8
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    Cited by:

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    2. 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.
    3. Bichler, Martin & Merting, Sören, 2018. "Truthfulness in advertising? Approximation mechanisms for knapsack bidders," European Journal of Operational Research, Elsevier, vol. 270(2), pages 775-783.
    4. 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.
    5. Komal Malik & Debasis Mishra, 2018. "Pareto efficient combinatorial auctions: dichotomous preferences without quasilinearity," Discussion Papers 18-06, Indian Statistical Institute, Delhi.
    6. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    7. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," Discussion Papers 17-03, Indian Statistical Institute, Delhi.
    8. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object allocation: Ex-post revenue maximization with no wastage," Working Papers e116, Tokyo Center for Economic Research.
    9. Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    10. Yu Zhou & Shigehiro Serizawa, 2016. "Strategy-Proofness and Efficiency for Non-quasi-linear Common-Tiered-Object Preferences: Characterization of Minimum Price Rule," ISER Discussion Paper 0971, Institute of Social and Economic Research, Osaka University.
    11. 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.
    12. 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).
    13. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    14. 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.

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