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Citations for "A Tale of Two Mechanisms: Student Placement"

by Balinski, Michel & Sonmez, Tayfun

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  1. Thayer Morrill, 2015. "Two simple variations of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 123-140, September.
  2. Azevedo, Eduardo M., 2014. "Imperfect competition in two-sided matching markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 207-223.
  3. Özgür Kıbrıs & İpek Tapkı, 2014. "A mechanism design approach to allocating central government funds among regional development agencies," Review of Economic Design, Springer;Society for Economic Design, vol. 18(3), pages 163-189, September.
  4. Alcalde, José & Romero-Medina, Antonio, 2011. "Fair School Placement," QM&ET Working Papers 11-1, University of Alicante, D. Quantitative Methods and Economic Theory.
  5. John Kennes & Daniel Monte & Norovsambuu Tumennasan, 2015. "Dynamic Matching Markets and the Deferred Acceptance Mechanism," Economics Working Papers 2015-23, Department of Economics and Business Economics, Aarhus University.
  6. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
  7. EHLERS, Lars & KLAUS, Bettina, 2005. "Consistent House Allocation," Cahiers de recherche 08-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Yeon-Koo Che & Fuhito Kojima, 2008. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Cowles Foundation Discussion Papers 1677, Cowles Foundation for Research in Economics, Yale University.
  9. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
  10. 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 1954-78, December.
  11. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  12. repec:ner:carlos:info:hdl:10016/847 is not listed on IDEAS
  13. Haluk Ergin & Tayfun Sönmez, 2005. "Games of School Choice under the Boston Mechanism," Boston College Working Papers in Economics 619, Boston College Department of Economics.
  14. Selim, Tarek & Salem, Sherif, 2009. "Student Placement in Egyptian Colleges," MPRA Paper 17596, University Library of Munich, Germany.
  15. Yan Chen & Tayfun Sönmez, 2004. "School Choice: An Experimental Study," Boston College Working Papers in Economics 622, Boston College Department of Economics.
  16. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
  17. Hafalir, Isa E. & Hakimov, Rustamdjan & Kübler, Dorothea & Kurino, Morimitsu, 2014. "College admissions with entrance exams: Centralized versus decentralized," Discussion Papers, Research Unit: Market Behavior SP II 2014-208, Social Science Research Center Berlin (WZB).
  18. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
  19. Katarina Cechlarova & Bettina Klaus & David F.Manlove, 2016. "Pareto optimal matchings of students to courses in the presence of prerequisites," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 16.04, Université de Lausanne, Faculté des HEC, DEEP.
  20. Roth, Alvin, 2008. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," Scholarly Articles 2579651, Harvard University Department of Economics.
  21. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 2006-04, Universite de Montreal, Departement de sciences economiques.
  22. Braun Sebastian & Dwenger Nadja & Kübler Dorothea, 2010. "Telling the Truth May Not Pay Off: An Empirical Study of Centralized University Admissions in Germany," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-38, March.
  23. Pereyra, Juan Sebastián, 2013. "A dynamic school choice model," Games and Economic Behavior, Elsevier, vol. 80(C), pages 100-114.
  24. Guillen, Pablo & Kesten, Onur, 2008. "On-Campus Housing: Theory vs. Experiment," Working Papers 2008-02, University of Sydney, School of Economics.
  25. Sebastian Braun & Nadja Dwenger & Dorothea Kübler, 2007. "Telling the Truth May Not Pay Off," Discussion Papers of DIW Berlin 759, DIW Berlin, German Institute for Economic Research.
  26. Lars Ehlers & Bettina Klaus, 2013. "House Allocation via Deferred-Acceptance," Cahiers de recherche 06-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  27. Alcalde, José & Romero-Medina, Antonio, 2015. "Strategy-Proof Fair School Placement," MPRA Paper 62831, University Library of Munich, Germany.
  28. László Á. Kóczy, 2009. "Központi felvételi rendszerek: Taktikázás és stabilitás," Working Paper Series 0901, Óbuda University, Keleti Faculty of Business and Management.
  29. Péter Biró & Sofya Kiselgof, 2015. "College admissions with stable score-limits," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 727-741, December.
  30. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-89, June.
  31. YuenLeng Chow & Isa Hafalir & Abdullah Yavas, . "Auctions versus Negotiated Sale: Evidence from Real Estate Sales," GSIA Working Papers 2012-E22, Carnegie Mellon University, Tepper School of Business.
  32. B. Evci, 2014. "A new dynamic mechanism to the marriage problem with a variant," Working Papers wp973, Dipartimento Scienze Economiche, Universita' di Bologna.
  33. Lars EHLERS & Bettina KLAUS, 2014. "Object Allocation via Deferred-Acceptance : Strategy-Proofness and Comparative Statics," Cahiers de recherche 14-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  34. Boudreau, James W., 2010. "Stratification and growth in agent-based matching markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 168-179, August.
  35. Lars Ehlers & Bettina Klaus, 2003. "Efficient Priority Rules," Working Papers 103, Barcelona Graduate School of Economics.
  36. Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
  37. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
  38. Doruk İriş & İpek Özkal-Sanver, 2011. "Manilulation via endowments in university-admission problem," Economics Bulletin, AccessEcon, vol. 31(4), pages 2952-2958.
  39. Che, Yeon-Koo & Kim, Jinwoo & Kojima, Fuhito, 2015. "Efficient assignment with interdependent values," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 54-86.
  40. EHLERS, Lars, 2009. "Manipulation via Capacities Revisited," Cahiers de recherche 2009-03, Universite de Montreal, Departement de sciences economiques.
  41. Bettina Klaus & Flip Klijn, 2011. "Local and Global Consistency Properties for Student Placement," Working Papers 538, Barcelona Graduate School of Economics.
  42. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
  43. Tommy Andersson & Lars-Gunnar Svensson, 2008. "Weakly fair allocations and strategy-proofness," Review of Economic Design, Springer;Society for Economic Design, vol. 11(4), pages 321-338, February.
  44. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
  45. Tayfun Sonmez & Parag Pathak (MIT), 2011. "Admissions Reform at Chicago's Selective High Schools: Comparing Mechanisms by their Vulnerability to Manipulation," EcoMod2011 2954, EcoMod.
  46. Carvalho, José-Raimundo & Magnac, Thierry & Xiong, Qizhou, 2014. "College Choice Allocation Mechanisms: Structural Estimates and Counterfactuals," IZA Discussion Papers 8550, Institute for the Study of Labor (IZA).
  47. John Kennes Jr. & Daniel Monte Jr. & Norovsambuu Tumennasan Jr., 2014. "The Day Care Assignment: A Dynamic Matching Problem," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 362-406, November.
  48. Lars Ehlers & Bettina Klaus, 2012. "Strategy-Proofness makes the Difference: Deferred-Acceptance with Responsive Priorities," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 12.06, Université de Lausanne, Faculté des HEC, DEEP.
  49. Fack, Gabrielle & Grenet, Julien & He, Yinghua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice," TSE Working Papers 15-607, Toulouse School of Economics (TSE).
  50. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
  51. Lars Ehlers & Bettina Klaus, 2013. "House Allocation via Deferred-Acceptance (N.B.: This paper has been extended and results are now contained in working paper 14.08.)," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.10, Université de Lausanne, Faculté des HEC, DEEP.
  52. Mehmet Ekmekci & M. Bumin Yenmez, . "Integrating Schools for Centralized Admissions," GSIA Working Papers 2014-E20, Carnegie Mellon University, Tepper School of Business.
  53. Umut Mert Dur & M. Utku Ünver, 2012. "Two-Sided Matching via Balanced Exchange: Tuition and Worker Exchanges," Boston College Working Papers in Economics 815, Boston College Department of Economics, revised 11 Mar 2015.
  54. Guillaume Haeringer & Vincent Iehlé, 2014. "Two-sided matching with one-sided preferences," Working Papers halshs-00980794, HAL.
  55. Andersson, Tommy & Svensson, Lars-Gunnar, 2015. "Strategy-Proof House Allocation with Price Restrictions," Working Papers 2015:9, Lund University, Department of Economics, revised 27 Apr 2015.
  56. Parag A. Pathak & Tayfun Sönmez, 2011. "School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation," Boston College Working Papers in Economics 784, Boston College Department of Economics.
  57. Tang, Qianfeng & Yu, Jingsheng, 2014. "A new perspective on Kesten's school choice with consent idea," Journal of Economic Theory, Elsevier, vol. 154(C), pages 543-561.
  58. Yeon-Koo Che & Olivier Tercieux, 2015. "Efficiency and Stability in Large Matching Markets," Cowles Foundation Discussion Papers 2013, Cowles Foundation for Research in Economics, Yale University.
  59. Peter Biro & Sofya Kiselgof, 2013. "College admissions with stable score-limits," IEHAS Discussion Papers 1306, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  60. Matteo Triossi & Antonio Romero-Medina, 2006. "Ramón y Cajal: Mediation and Meritocracy," Carlo Alberto Notebooks 22, Collegio Carlo Alberto.
  61. Dinko Dimitrov & Emiliya Lazarova, 2009. "Coalitional Matchings," Economics Working Papers 09-05, Queen's Management School, Queen's University Belfast.
  62. Salem, Sherif Gamal, 2012. "Stability, efficiency and monotonicity in two-sided matching," MPRA Paper 37215, University Library of Munich, Germany.
  63. Matteo Triossi & Antonio Romero-Medina, 2010. "Non-revelation Mechanisms in Many-to-One Markets," Documentos de Trabajo 273, Centro de Economía Aplicada, Universidad de Chile.
  64. Fuhito Kojima & M. Utku Ünver, 2010. "The 'Boston' School-Choice Mechanism," Boston College Working Papers in Economics 729, Boston College Department of Economics, revised 08 Oct 2010.
  65. Onur Kesten, 2009. "Coalitional strategy-proofness and resource monotonicity for house allocation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 17-21, March.
  66. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
  67. Yenmez, M. Bumin & Yildirim, Muhammed Ali & Hafalir, Isa Emin, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
  68. Takumi Kongo, 2013. "An incompatibility between recursive unanimity and strategy-proofness in two-sided matching problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 461-478, February.
  69. Ozkal-Sanver, Ipek & Remzi Sanver, M., 2005. "Implementing matching rules by type pretension mechanisms," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 304-317, November.
  70. Ekrem Akkaya & Ayþe Mumcu, 2012. "Student Placement Problems: An Application to the ERASMUS Exchange Program," Bogazici Journal of Economics and Administrative Sciences, Bogazici University, Department of Economics, vol. 26(2), pages 63-82.
  71. Atila Abdulkadiroglu & Parag Pathak & Alvin E. Roth & Tayfun Sonmez, 2006. "Changing the Boston School Choice Mechanism," NBER Working Papers 11965, National Bureau of Economic Research, Inc.
  72. Min Zhu, 2013. "College Admissions in China : A Mechanism Design Perspective," Working Papers halshs-00860931, HAL.
  73. Alcalde, Jose, 2013. "Random Housing with Existing Tenants," QM&ET Working Papers 13-5, University of Alicante, D. Quantitative Methods and Economic Theory.
  74. Guillen, Pablo & Kesten, Onur, 2010. "Matching Markets with Mixed Ownership: The Case for A Real-life Assignment Mechanism," Working Papers 2010-01, University of Sydney, School of Economics.
  75. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
  76. Bettina Klaus & Flip Klijn, 2004. "Fair and Efficient Student Placement with Couples," Working Papers 145, Barcelona Graduate School of Economics.
  77. Min Zhu, 2013. "College Admissions in China : A Mechanism Design Perspective," Working Papers 1327, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  78. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
  79. Jaimie W. Lien & Jie Zheng & Xiaohan Zhong, 2016. "Preference submission timing in school choice matching: testing fairness and efficiency in the laboratory," Experimental Economics, Springer, vol. 19(1), pages 116-150, March.
  80. 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, 02.
  81. Aradhna Krishna & M. Utku Ünver, 2008. "Research Note—Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies," Marketing Science, INFORMS, vol. 27(2), pages 262-282, 03-04.
  82. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506 Elsevier.
  83. Fuhito Kojima, 2008. "Games of school choice under the Boston mechanism with general priority structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 357-365, October.
  84. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186 - 219.
  85. Alcalde, Jose & Silva-Reus, José Ángel, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, University of Alicante, D. Quantitative Methods and Economic Theory.
  86. Huberto Ennis & Alberto Porto, 2001. "Igualdad de Oportunidades e Ingreso a la Universidad Pública en la Argentina," Department of Economics, Working Papers 030, Departamento de Economía, Facultad de Ciencias Económicas, Universidad Nacional de La Plata.
  87. Kojima, Fuhito, 2008. "The law of aggregate demand and welfare in the two-sided matching market," Economics Letters, Elsevier, vol. 99(3), pages 581-584, June.
  88. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
  89. Andersson, Tommy & Svensson, Lars-Gunnar, 2015. "Sequential Rules for House Allocation with Price Restrictions," Working Papers 2015:18, Lund University, Department of Economics, revised 14 Oct 2015.
  90. Andersson, Tommy & Svensson, Lars-Gunnar, 2012. "Non-Manipulable House Allocation with Rent Control," Working Papers 2012:18, Lund University, Department of Economics, revised 10 Jun 2013.
  91. Tayfun Sönmez & Tobias B. Switzer, 2011. "Matching with (Branch-of-Choice) Contracts at United States Military Academy," Boston College Working Papers in Economics 782, Boston College Department of Economics.
  92. Dur, Umut, 2012. "A Characterization of the Top Trading Cycles Mechanism for the School Choice Problem," MPRA Paper 41366, University Library of Munich, Germany.
  93. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
  94. Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 27-33.
  95. Onur Kesten, 2012. "On two kinds of manipulation for school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 677-693, November.
  96. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 3-24, August.
  97. Manjunath, Vikram & Turhan, Bertan, 2016. "Two school systems, one district: What to do when a unified admissions process is impossible," Games and Economic Behavior, Elsevier, vol. 95(C), pages 25-40.
  98. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 561-589, August.
  99. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
  100. Alcalde, Jose & Romero-Medina, Antonio, 2011. "Re-Reforming the Bostonian System: A Novel Approach to the Schooling Problem," MPRA Paper 28206, University Library of Munich, Germany.
  101. J.-R. Carvalho & T. Magnac & Qizhou Xiong, 2016. "College Choice and the Selection of Mechanisms: A Structural Empirical Analysis," IWH Discussion Papers 3, Halle Institute for Economic Research.
  102. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
  103. Hatfield, John William & Kojima, Fuhito, 2009. "Group incentive compatibility for matching with contracts," Games and Economic Behavior, Elsevier, vol. 67(2), pages 745-749, November.
  104. Thayer Morrill, 2013. "An alternative characterization of the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 19-28, February.
  105. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
  106. Azar Abizada & Siwei Chen, 2015. "Stability and strategy-proofness for college admissions with an eligibility criterion," Review of Economic Design, Springer;Society for Economic Design, vol. 19(1), pages 47-66, March.
  107. Estrada, Ricardo, 2016. "The Effect of the Increasing Demand for Elite Schools on Stratification," Economics Working Papers MWP2016/02, European University Institute.
  108. Murat Sertel, 2000. "Manipulability of the Men-(Women) Optimal Matching Rule via Endowments," Working Papers 0014, Department of Economics, Bilkent University.
  109. Li Chen & Juan Sebastian Pereyra Barreiro, 2015. "Self-Selection in School Choice," Working Papers ECARES ECARES 2015-52, ULB -- Universite Libre de Bruxelles.
  110. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2012. "Promoting School Competition Through School Choice: A Market Design Approach," Discussion Papers 12-036, Stanford Institute for Economic Policy Research.
  111. 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.
  112. Kesten, Onur & Kurino, Morimitsu, 2012. "On the (im)possibility of improving upon the student-proposing deferred acceptance mechanism," Discussion Papers, Research Unit: Market Behavior SP II 2012-202, Social Science Research Center Berlin (WZB).
  113. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
  114. António Neto, 2015. "The Portuguese high school match," Economics Bulletin, AccessEcon, vol. 35(3), pages 1765-1771.
  115. Zhu, Min, 2014. "College admissions in China: A mechanism design perspective," China Economic Review, Elsevier, vol. 30(C), pages 618-631.
  116. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 14.07, Université de Lausanne, Faculté des HEC, DEEP.
  117. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
  118. Kojima, Fuhito, 2012. "School choice: Impossibilities for affirmative action," Games and Economic Behavior, Elsevier, vol. 75(2), pages 685-693.
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