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An assignment model with local constraints: Competitive equilibrium and ascending auction

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  • Pan, Lijun
  • Peng, Linyu
  • Zhou, Yu

Abstract

We consider an assignment model where each agent has unit-demand quasi-linear preferences and may face some local constraint, i.e., her possible assignment is restricted to a subset of items. Our model takes the assignment models without and with outside options, e.g., Andersson (2007) and Andersson et al. (2013), as special cases. We show that local constraints may lead to the non-existence of competitive equilibrium (CE), and provide a sufficient and necessary condition that ensures its existence. We establish the lattice of CE prices. Besides, an ascending auction is proposed, either finding a CE or validating its non-existence in finitely many steps. It generalizes Andersson et al. (2013)’s auction by adjusting increments stepwise.

Suggested Citation

  • Pan, Lijun & Peng, Linyu & Zhou, Yu, 2020. "An assignment model with local constraints: Competitive equilibrium and ascending auction," Economics Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:ecolet:v:188:y:2020:i:c:s0165176519304562
    DOI: 10.1016/j.econlet.2019.108905
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    References listed on IDEAS

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    1. T. Andersson & C. Andersson & A. Talman, 2013. "Sets in excess demand in simple ascending auctions with unit-demand bidders," Annals of Operations Research, Springer, vol. 211(1), pages 27-36, December.
    2. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 227-245, August.
    3. Andersson, Tommy & Svensson, Lars-Gunnar, 2008. "Non-manipulable assignment of individuals to positions revisited," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 350-354, November.
    4. Mishra, Debasis & Talman, Dolf, 2010. "Characterization of the Walrasian equilibria of the assignment model," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 6-20, January.
    5. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    6. Mustafa Oǧuz Afacan, 2019. "Matching with restricted trade," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 957-977, September.
    7. Andersson, Tommy, 2007. "An algorithm for identifying fair and optimal allocations," Economics Letters, Elsevier, vol. 96(3), pages 337-342, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Assignment model; Local constraints; Competitive equilibrium; Existence; Lattice; Ascending auction;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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