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An Ascending Multi-Item Auction with Financially Constrained Bidders

Author

Listed:
  • Gerard van der Laan

    (VU University Amsterdam)

  • Zaifu Yang

    (Yokohama National University)

Abstract

A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium usually fails to exist and also the existing auctions might fail to allocate the items among the bidders. In this paper we first introduce a rationed equilibrium for a market situation with financially constrained bidders. Succeedingly we propose an ascending auction mechanism that always results in an equilibrium allocation and price system. By starting with the reservation price of each item, the auctioneer announces the current prices of the items in each step and the bidders respond with their demand sets at these prices. As long as there is overdemand, the auctioneer adjusts prices upwards for overdemanded items until a price system is reached at which either there is an underdemanded set, or there is neither overdemand nor underdemand anymore. In the latter case the auction stops. In the former case, precisely one item will be sold, the bidder buying the item leaves the auction and the auction continues with the remaining items and the remaining bidders. We prove that the auction finds a rationed equilibrium in a finite number of steps. In addition, we derive various properties of the allocation and price system obtained by the auction.

Suggested Citation

  • Gerard van der Laan & Zaifu Yang, 2008. "An Ascending Multi-Item Auction with Financially Constrained Bidders," Tinbergen Institute Discussion Papers 08-017/1, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20080017
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    References listed on IDEAS

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    Citations

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    Cited by:

    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. P. Jean‐Jacques Herings & Yu Zhou, 2022. "Competitive Equilibria In Matching Models With Financial Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 777-802, May.
    3. A. Talman & Zaifu Yang, 2015. "An efficient multi-item dynamic auction with budget constrained bidders," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 769-784, August.
    4. van der Laan, G. & Talman, Dolf & Yang, Z., 2018. "Equilibrium in the Assignment Market under Budget Constraints," Other publications TiSEM 965cd6c8-4f09-47c4-a101-1, Tilburg University, School of Economics and Management.
    5. Tommy Andersson & Lars Ehlers, 2022. "An algorithm for identifying least manipulable envy‐free and budget‐balanced allocations in economies with indivisibilities," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 50-60, March.
    6. Andersson, T. & Erlanson, A. & Gudmundsson, J. & Habis, H. & Ingebretsen Carlson, J. & Kratz, J., 2014. "A method for finding the maximal set in excess demand," Economics Letters, Elsevier, vol. 125(1), pages 18-20.
    7. Zhou, Yu, 2017. "A multi-item auction with budget-constrained bidders and price controls," Economics Letters, Elsevier, vol. 155(C), pages 76-79.
    8. Andersson, Tommy & Yang, Zaifu & Zhang, Dongmo, 2015. "How to efficiently allocate houses under price controls?," Economics Letters, Elsevier, vol. 130(C), pages 97-99.
    9. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    10. van der Laan, G. & Talman, Dolf & Yang, Z., 2018. "Equilibrium in the Assignment Market under Budget Constraints," Discussion Paper 2018-046, Tilburg University, Center for Economic Research.
    11. Jianxin Rong & Ning Sun & Dazhong Wang, 2019. "A New Evaluation Criterion for Allocation Mechanisms with Application to Vehicle License Allocations in China," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 4(1), pages 39-86, November.
    12. Andrew MACKENZIE & Yu ZHOU, 2022. "Tract Housing, The Core, And Pendulum Auctions," Discussion papers e-22-005, Graduate School of Economics , Kyoto University.
    13. Ashlagi Itai & Braverman Mark & Hassidim Avinatan & Lavi Ron & Tennenholtz Moshe, 2010. "Position Auctions with Budgets: Existence and Uniqueness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-32, May.
    14. Zaifu Yang & Jingsheng Yu, 2018. "Efficient Ascending Menu Auctions with Budget Constrained Bidders," Discussion Papers 18/09, Department of Economics, University of York.
    15. Eleni Batziou & Martin Bichler & Maximilian Fichtl, 2022. "Core-Stability in Assignment Markets with Financially Constrained Buyers," Papers 2205.06132, arXiv.org.

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    More about this item

    Keywords

    Ascending auction; multi-item auction; financial constraint;
    All these keywords.

    JEL classification:

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

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