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Collusion-proof mechanisms for multi-unit procurement

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  • Hagen, Martin

Abstract

A principal wants to procure multiple homogeneous units from finitely many agents. Each agent has an increasing and convex cost function, whose exact shape is unknown to the principal. Utility is quasilinear in money. We study which mechanisms are strategy-proof and robust to collusion, both when the agents can exchange money and physical units (reallocation-proofness) and when they cannot (group strategy-proofness). To achieve reallocation-proofness, the principal must offer the agents a fixed price per unit. While group-strategy-proof mechanisms can be more complex, they are inefficient and run the risk of procuring no units at all. We characterize the set of group-strategy-proof and anonymous mechanisms with a uniform price. A standout feature is that the number of potential prices is bounded above by the number of agents.

Suggested Citation

  • Hagen, Martin, 2023. "Collusion-proof mechanisms for multi-unit procurement," Games and Economic Behavior, Elsevier, vol. 138(C), pages 281-298.
    • Handle: RePEc:eee:gamebe:v:138:y:2023:i:c:p:281-298
    DOI: 10.1016/j.geb.2023.01.002
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    as
    1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    2. 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.
    3. Chen, Jing & Micali, Silvio, 2012. "Collusive dominant-strategy truthfulness," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1300-1312.
    4. Deckelbaum, Alan & Micali, Silvio, 2017. "Collusion, efficiency, and dominant strategies," Games and Economic Behavior, Elsevier, vol. 103(C), pages 83-93.
    5. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1366-1400.
    6. Che, Yeon-Koo & Kim, Jinwoo, 2009. "Optimal collusion-proof auctions," Journal of Economic Theory, Elsevier, vol. 144(2), pages 565-603, March.
    7. Conan Mukherjee, 2013. "Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 131-163, February.
    8. Duygu Yengin, 2012. "Egalitarian-equivalent Groves mechanisms in the allocation of heterogenous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 137-160, January.
    9. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    10. Hashimoto, Kazuhiko & Saitoh, Hiroki, 2015. "Strategy-proof cost sharing under increasing returns: Improvement of the supremal welfare loss," Games and Economic Behavior, Elsevier, vol. 89(C), pages 101-121.
    11. Duygu Yengin, 2013. "Identical Preferences Lower Bound for Allocation of Heterogenous Tasks and NIMBY Problems," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 580-601, August.
    12. Conan Mukherjee, 2014. "Fair and group strategy-proof good allocation with money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 289-311, February.
    13. Kuzmics, Christoph & Steg, Jan-Henrik, 2017. "On public good provision mechanisms with dominant strategies and balanced budget," Journal of Economic Theory, Elsevier, vol. 170(C), pages 56-69.
    14. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    15. Yeon-Koo Che & Jinwoo Kim, 2006. "Robustly Collusion-Proof Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1063-1107, July.
    16. Juarez, Ruben, 2013. "Group strategyproof cost sharing: The role of indifferences," Games and Economic Behavior, Elsevier, vol. 82(C), pages 218-239.
    17. Mehta, Aranyak & Roughgarden, Tim & Sundararajan, Mukund, 2009. "Beyond Moulin mechanisms," Games and Economic Behavior, Elsevier, vol. 67(1), pages 125-155, September.
    18. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    19. Grossman, Zachary & Pincus, Jonathan & Shapiro, Perry & Yengin, Duygu, 2019. "Second-best mechanisms for land assembly and hold-out problems," Journal of Public Economics, Elsevier, vol. 175(C), pages 1-16.
    20. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    21. Conan Mukherjee, 2020. "On group strategyproof and optimal object allocation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 289-304, October.
    22. Jean-Jacques Laffont & David Martimort, 1997. "Collusion under Asymmetric Information," Econometrica, Econometric Society, vol. 65(4), pages 875-912, July.
    23. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    24. Jean-Jacques Laffont & David Martimort, 2000. "Mechanism Design with Collusion and Correlation," Econometrica, Econometric Society, vol. 68(2), pages 309-342, March.
    25. Jerry Green & Jean-Jacques Laffont, 1979. "On Coalition Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 243-254.
    26. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.
    27. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
    28. Brenner, Menachem & Galai, Dan & Sade, Orly, 2009. "Sovereign debt auctions: Uniform or discriminatory?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 267-274, March.
    29. Marhsall, Robert C. & Marx, Leslie M., 2014. "The Economics of Collusion: Cartels and Bidding Rings," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262525941, December.
    30. Schummer, James, 2000. "Manipulation through Bribes," Journal of Economic Theory, Elsevier, vol. 91(2), pages 180-198, April.
    31. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 287-309, August.
    32. Hideki Mizukami, 2003. "On the constancy of bribe-proof solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 211-217, August.
    33. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
    34. Hagerty, Kathleen M. & Rogerson, William P., 1987. "Robust trading mechanisms," Journal of Economic Theory, Elsevier, vol. 42(1), pages 94-107, June.
    35. Felix J. Bierbrauer & Martin F. Hellwig, 2016. "Robustly Coalition-Proof Incentive Mechanisms for Public Good Provision are Voting Mechanisms and Vice Versa," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1440-1464.
    36. Murat Atlamaz & Duygu Yengin, 2008. "Fair Groves mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 573-587, December.
    37. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    38. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    39. Hiroki Shinozaki, 2022. "No price envy in the multi-unit object allocation problem with non-quasi-linear preferences," ISER Discussion Paper 1164, Institute of Social and Economic Research, Osaka University.
    40. Elaine Bennett & David Conn, 1977. "The group incentive properties of mechanisms for the provision of public goods," Public Choice, Springer, vol. 29(2), pages 95-102, March.
    41. Mitra, Manipushpak & Mutuswami, Suresh, 2011. "Group strategyproofness in queueing models," Games and Economic Behavior, Elsevier, vol. 72(1), pages 242-254, May.
    42. Hagen, Martin & Hernando-Veciana, Ángel, 2021. "Multidimensional bargaining and posted prices," Journal of Economic Theory, Elsevier, vol. 196(C).
    43. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
    44. 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.
    45. Mutuswami, Suresh, 2005. "Strategyproofness, Non-Bossiness and Group Strategyproofness in a cost sharing model," Economics Letters, Elsevier, vol. 89(1), pages 83-88, October.
    46. Nanyang Bu, 2016. "Joint misrepresentation with bribes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 115-125, January.
    47. Burkett, Justin & Woodward, Kyle, 2020. "Uniform price auctions with a last accepted bid pricing rule," Journal of Economic Theory, Elsevier, vol. 185(C).
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    More about this item

    Keywords

    Mechanism design; Procurement; Collusion; Group strategy-proofness; Reallocation-proofness;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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