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Ex-post Optimal Knapsack Procurement

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  • Jarman, Felix
  • Meisner, Vincent

Abstract

We consider a budget-constrained mechanism designer who wants to select an optimal subset of projects to maximize her utility. Project costs are private information and the value the designer derives from their provision may vary. In this allocation problem the choice of projects - both which and how many - is endogenously determined by the mechanism. The designer faces hard ex-post constraints: The participation and budget constraint must hold for each possible outcome while the mechanism must be implementable in dominant strategies. We derive the class of optimal mechanisms and show that it allows an implementation through a descending clock auction. Only in the case of symmetric projects, price clocks do descend synchronously such that always the cheapest projects are executed. The asymmetric case, where values or costs are asymmetrically distributed, features a novel tradeoff between quantity and quality. Interestingly, this tradeoff mitigates the distortion due to the informational asymmetry compared to environments where quantity is exogenous.

Suggested Citation

  • Jarman, Felix & Meisner, Vincent, 2015. "Ex-post Optimal Knapsack Procurement," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112903, Verein für Socialpolitik / German Economic Association.
  • Handle: RePEc:zbw:vfsc15:112903
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    1. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 511-533.
    2. Tilman Börgers & Peter Norman, 2009. "A note on budget balance under interim participation constraints: the case of independent types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 477-489, June.
    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    4. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    5. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 1-21.
    6. Strausz, Roland, 2003. "Deterministic mechanisms and the revelation principle," Economics Letters, Elsevier, vol. 79(3), pages 333-337, June.
    7. Mookherjee, Dilip & Reichelstein, Stefan, 1992. "Dominant strategy implementation of Bayesian incentive compatible allocation rules," Journal of Economic Theory, Elsevier, vol. 56(2), pages 378-399, April.
    8. Baron, David P & Myerson, Roger B, 1982. "Regulating a Monopolist with Unknown Costs," Econometrica, Econometric Society, vol. 50(4), pages 911-930, July.
    9. Luton, Richard & McAfee, R. Preston, 1986. "Sequential procurement auctions," Journal of Public Economics, Elsevier, vol. 31(2), pages 181-195, November.
    10. Ensthaler, Ludwig & Giebe, Thomas, 2014. "A dynamic auction for multi-object procurement under a hard budget constraint," Research Policy, Elsevier, vol. 43(1), pages 179-189.
    11. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    12. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    13. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    14. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    15. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    16. de Castro, Luciano I. & de Frutos, María-Angeles, 2010. "How to translate results from auctions to procurements," Economics Letters, Elsevier, vol. 106(2), pages 115-118, February.
    17. John Ledyard & David Porter & Randii Wessen, 2000. "A Market-Based Mechanism for Allocating Space Shuttle Secondary Payload Priority," Experimental Economics, Springer;Economic Science Association, vol. 2(3), pages 173-195, March.
    18. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    19. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    20. , & , & ,, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    21. Jeffrey C. Ely & Kim-Sau Chung, 2002. "Ex-Post Incentive Compatible Mechanism Design," Discussion Papers 1339, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    22. Bernard Caillaud & Jacques Robert, 2005. "Implementation of the revenue-maximizing auction by an ignorant seller," Review of Economic Design, Springer;Society for Economic Design, vol. 9(2), pages 127-143, April.
    23. Ensthaler, Ludwig & Giebe, Thomas, 2014. "Bayesian optimal knapsack procurement," European Journal of Operational Research, Elsevier, vol. 234(3), pages 774-779.
    24. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
    25. HervÊ Moulin, 1999. "Incremental cost sharing: Characterization by coalition strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 279-320.
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    Cited by:

    1. Haoran He & Yefeng Chen, 2021. "Auction mechanisms for allocating subsidies for carbon emissions reduction: an experimental investigation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 387-430, August.
    2. Jarman, Felix & Meisner, Vincent, 2017. "Deterministic mechanisms, the revelation principle, and ex-post constraints," Economics Letters, Elsevier, vol. 161(C), pages 96-98.
    3. Paul Dütting & Vasilis Gkatzelis & Tim Roughgarden, 2017. "The Performance of Deferred-Acceptance Auctions," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 897-914, November.

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    More about this item

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D45 - Microeconomics - - Market Structure, Pricing, and Design - - - Rationing; Licensing
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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