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Foundations of Pseudomarkets: Walrasian Equilibria for Discrete Resources

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  • Pycia, Marek
  • Miralles, Antonio

Abstract

We study the assignment of objects in environments without transfers allowing for single-unit and general multi-unit demands, and any linear constraints, thus covering a wide range of applied environments, from school choice to course allocation. We establish the Second Welfare Theorem for these environments despite them failing the local non-satiation condition that previous studies of the Second Welfare Theorem relied on. We also prove a strong version of the First Welfare Theorem. We thus show that the link between efficiency and decentralization through prices is valid in environments without transfers, and hence provide a foundation for pseudomarket- based market design by showing that the restriction to such mechanisms is without loss of generality.

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  • Pycia, Marek & Miralles, Antonio, 2020. "Foundations of Pseudomarkets: Walrasian Equilibria for Discrete Resources," CEPR Discussion Papers 15161, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:15161
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    1. Elizabeth Baldwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Papers 2006.16939, arXiv.org.
    2. Schlegel, Jan Christoph & Mamageishvili, Akaki, 2020. "Welfare theorems for random assignments with priorities," Games and Economic Behavior, Elsevier, vol. 124(C), pages 62-81.
    3. Vijay V. Vazirani & Mihalis Yannakakis, 2020. "Computational Complexity of the Hylland-Zeckhauser Scheme for One-Sided Matching Markets," Papers 2004.01348, arXiv.org, revised Apr 2020.
    4. Federico Echenique & Antonio Miralles & Jun Zhang, 2021. "Constrained Pseudo-Market Equilibrium," American Economic Review, American Economic Association, vol. 111(11), pages 3699-3732, November.
    5. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    6. Yinghua He & Antonio Miralles & Marek Pycia & Jianye Yan, 2018. "A Pseudo-Market Approach to Allocation with Priorities," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 272-314, August.
    7. Eduardo M Azevedo & Eric Budish, 2019. "Strategy-proofness in the Large," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 81-116.
    8. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    9. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    10. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    11. Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
    12. Hafalir, Isa & Miralles, Antonio, 2015. "Welfare-maximizing assignment of agents to hierarchical positions," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 253-270.
    13. Makowski, Louis & Ostroy, Joseph M. & Segal, Uzi, 1999. "Efficient Incentive Compatible Economies Are Perfectly Competitive," Journal of Economic Theory, Elsevier, vol. 85(2), pages 169-225, April.
    14. Andreu Mas-Colell, 1992. "Equilibrium Theory with Possibly Satiated Preferences," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 9, pages 201-213, Palgrave Macmillan.
    15. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    16. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    17. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    18. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    19. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    20. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    21. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    22. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    23. Eric Maskin & Kevin Roberts, 2008. "On the fundamental theorems of general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 233-240, May.
    24. Tommy Andersson & Lars Ehlers, 2020. "Assigning Refugees to Landlords in Sweden: Efficient, Stable, and Maximum Matchings," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(3), pages 937-965, July.
    25. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    26. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    27. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaia, 2019. "Dividing bads under additive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 395-417, March.
    28. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    29. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    30. Schlegel, J. C. & Mamageishvili, A., 2017. "Welfare theorems for random assignments with priorities," Working Papers 17/05, Department of Economics, City University London.
    31. Chiaki Hara, 2005. "Existence of Equilibria in Economies with Bads," Econometrica, Econometric Society, vol. 73(2), pages 647-658, March.
    32. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    33. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    34. Itai Ashlagi & Peng Shi, 2016. "Optimal Allocation Without Money: An Engineering Approach," Management Science, INFORMS, vol. 62(4), pages 1078-1097, April.
    35. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    36. Moshe Babaioff & Noam Nisan & Inbal Talgam-Cohen, 2021. "Competitive Equilibrium with Indivisible Goods and Generic Budgets," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 382-403, February.
    37. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    38. Thomson, William & Zhou, Lin, 1993. "Consistent Solutions in Atomless Economies," Econometrica, Econometric Society, vol. 61(3), pages 575-587, May.
    39. Carroll, Gabriel, 2010. "An efficiency theorem for incompletely known preferences," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2463-2470, November.
    40. Florig, Michael & Rivera, Jorge, 2010. "Core equivalence and welfare properties without divisible goods," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 467-474, July.
    41. Antonio Miralles, 2017. "Ex-ante efficiency in assignments with seniority rights," Review of Economic Design, Springer;Society for Economic Design, vol. 21(1), pages 33-48, March.
    42. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    43. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    44. Anderson, Robert M, 1988. "The Second Welfare Theorem with Nonconvex Preferences," Econometrica, Econometric Society, vol. 56(2), pages 361-382, March.
    45. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    46. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    47. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    48. Andersson, Tommy & Ehlers, Lars, 2016. "Assigning Refugees to Landlords in Sweden: Efficient Stable Maximum Matchings," Working Papers 2016:18, Lund University, Department of Economics, revised 27 Aug 2018.
    49. Atila Abdulkadiroğlu & Nikhil Agarwal & Parag A. Pathak, 2017. "The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match," American Economic Review, American Economic Association, vol. 107(12), pages 3635-3689, December.
    50. Philip J. Reny, 2017. "Assignment Problems," Journal of Political Economy, University of Chicago Press, vol. 125(6), pages 1903-1914.
    51. David Delacrétaz & Scott Duke Kominers & Alexander Teytelboym, 2023. "Matching Mechanisms for Refugee Resettlement," American Economic Review, American Economic Association, vol. 113(10), pages 2689-2717, October.
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    Cited by:

    1. Marek Pycia & M Bumin Yenmez, 2023. "Matching with Externalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 948-974.
    2. Julien Combe & Vladyslav Nora & Olivier Tercieux, 2021. "Dynamic assignment without money: Optimality of spot mechanisms," Working Papers 2021-11, Center for Research in Economics and Statistics.
    3. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. Combe, Julien & Nora, Vladyslav & Tercieux, Olivier, 0. "Dynamic assignment without money: optimality of spot mechanisms," Theoretical Economics, Econometric Society.
    5. Caterina Calsamiglia & Francisco Martínez-Mora & Antonio Miralles, 2021. "Random assignments and outside options," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 557-566, October.

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    More about this item

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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