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Robust group strategy-proof rules in the object allocation problem with money: The role of tie-breaking rules

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  • Shinozaki, Hiroki

Abstract

We study the object allocation problem with money. The owner owns identical objects. Each agent receives at most one unit of the object, and has a preference that is not necessarily quasi-linear. Recently, Kivinen and Tumennasan (2021) propose a group incentive property that they call robust group strategy-proofness. It takes into account a coalitional manipulation with which a coalition agrees without knowing the other agents’ preferences. We propose a generalized Vickrey rule with lowest priority agents that is associated with a tie-breaking rule such that for each coalitional report of preferences, there is an agent (a lowest priority agent) who has a chance to receive the object only after all the other members of the coalition receive the object. We show that the generalized Vickrey rules with lowest priority agents are the only rules satisfying robust group strategy-proofness, efficiency, individual rationality, and no subsidy for losers. Our result highlights the importance of the tie-breaking rules for robust group strategy-proofness, which contrasts with group strategy-proofness that a generalized Vickrey rule satisfies regardless of the tie-breaking rule.

Suggested Citation

  • Shinozaki, Hiroki, 2024. "Robust group strategy-proof rules in the object allocation problem with money: The role of tie-breaking rules," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    • Handle: RePEc:eee:mateco:v:115:y:2024:i:c:s0304406824001265
    DOI: 10.1016/j.jmateco.2024.103066
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    More about this item

    Keywords

    Robust group strategy-proofness; Tie-breaking rules; Priority; Efficiency; Generalized Vickrey rules; Multi-unit auctions;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • 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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