Market Design with Distributional Objectives

References

• [1] Abdulkadiroglu A, Grigoryan A (2021) Priority-based assignment with reserves and quotas. NBER Working Paper No. 28689, National Bureau of Economic Research, Cambridge, MA.Google Scholar
• [2] Aizerman MA, Malishevski AV (1981) General theory of best variants choice: Some aspects. IEEE Trans. Automatic Control 26(5):1030–1040.Crossref, Google Scholar
• [3] Alkan A, Gale D (2003) Stable schedule matching under revealed preference. J. Econom. Theory 112(2):289–306.Crossref, Google Scholar
• [4] Aygün O, Sönmez T (2013) Matching with contracts: Comment. Amer. Econom. Rev. 103(5):2050–2051.Crossref, Google Scholar
• [5] Aygün O, Turhan B (2017) Large-scale affirmative action in school choice: Admissions to IITs in India. Amer. Econom. Rev. 107(5):210–213.Crossref, Google Scholar
• [6] Aygün O, Turhan B (2020) Dynamic reserves in matching markets. J. Econom. Theory 188:105069.Crossref, Google Scholar
• [7] Bodoh-Creed AL, Hickman BR (2018) College assignment as a large contest. J. Econom. Theory 175:88–126.Crossref, Google Scholar
• [8] Brualdi RA (1969) Comments on bases in dependence structures. Bull. Australian Math. Soc. 1(2):161–167.Crossref, Google Scholar
• [9] Candogan O, Epitropou M, Vohra RV (2021) Competitive equilibrium and trading networks: A network flow approach. Oper. Res. 69(1):114–147.Link, Google Scholar
• [10] Çelebi O, Flynn JP (2025) Adaptive priority mechanisms. NBER Working Paper No. 34035, National Bureau of Economic Research, Cambridge, MA.Google Scholar
• [11] Chambers CP, Yenmez MB (2017) Choice and matching. Amer. Econom. J. Microeconomics 9(3):126–147.Crossref, Google Scholar
• [12] Che Y-K, Kim J, Kojima F (2019) Stable matching in large economies. Econometrica 87(1):65–110.Crossref, Google Scholar
• [13] Chen X, Li M (2021) M♮ convexity and its applications in operations. Oper. Res. 69(5):1396–1408.Link, Google Scholar
• [14] Correa J, Epstein R, Escobar J, Rios I, Bahamondes B, Bonet C, Epstein N, et al. (2019) School choice in Chile. Karlin A, Immorlica N, Johari R, eds. Proc. 2019 ACM Conf. Econom. Comput. EC‘19 (ACM, New York), 325–343.Google Scholar
• [15] Dien AE (2001) Civil service examinations: Evidence from the Northwest. Pearce S, Spiro A, Ebrey P, eds. Culture and Power in the Reconstitution of the Chinese Realm, 200–600, Harvard East Asian Monographs, 1st ed., vol. 200 (Harvard University Asia Center, Cambridge, MA), 99–121.Google Scholar
• [16] Echenique F, Yenmez MB (2015) How to control controlled school choice. Amer. Econom. Rev. 105(8):2679–2694.Crossref, Google Scholar
• [17] Eguchi A, Fujishige S, Tamura A (2003) A generalized Gale–Shapley algorithm for a discrete-concave stable-marriage model. Ibaraki T, Katoh N, Ono H, eds. Algorithms Comput. 14th Internat. Symposium, ISAAC 2003, Lecture Notes in Computer Science, vol. 2906 (Springer, Berlin), 495–504.Google Scholar
• [18] Ehlers L, Hafalir IE, Bumin Yenmez M, Yildirim MA (2014) School choice with controlled choice constraints: Hard bounds versus soft bounds. J. Econom. Theory 153:648–683.Crossref, Google Scholar
• [19] Farooq R, Shioura A (2005) A note on the equivalence between substitutability and M♮ convexity. Pacific J. Optim. 1:243–252.Google Scholar
• [20] Fleiner T (2001) A matroid generalization of the stable matching polytope. Aardal K, Gerards B, eds. Integer Programming and Combinatorial Optimization (Springer, Berlin), 105–114.Crossref, Google Scholar
• [21] Fujishige S (2005) Submodular Functions and Optimization (Elsevier, Amsterdam).Google Scholar
• [22] Gale D (1968) Optimal assignments in an ordered set: An application of matroid theory. J. Combin. Theory 4(2):176–180.Crossref, Google Scholar
• [23] Gale D, Shapley LS (1962) College admissions and the stability of marriage. Amer. Math. Monthly 69(1):9–15.Crossref, Google Scholar
• [24] Hafalir IE, Bumin Yenmez M, Yildirim MA (2013) Effective affirmative action in school choice. Theoret. Econom. 8(2):325–363.Crossref, Google Scholar
• [25] Hafalir IE, Kojima F, Bumin Yenmez M (2022) Interdistrict school choice: A theory of student assignment. J. Econom. Theory 201:105441.Crossref, Google Scholar
• [26] Hafalir IE, Kojima F, Bumin Yenmez M (2025) Market design with distributional objectives: Efficiency, incentives, and property rights. J. Econom. Theory 230:106099.Crossref, Google Scholar
• [27] Hatfield JW, Milgrom PR (2005) Matching with contracts. Amer. Econom. Rev. 95(4):913–935.Crossref, Google Scholar
• [28] Hatfield JW, Kominers SD, Nichifor A, Ostrovsky M, Westkamp A (2019) Full substitutability. Theoret. Econom. 14(4):1535–1590.Crossref, Google Scholar
• [29] Imamura K (2025) Meritocracy versus diversity. J. Econom. Theory 228:106047.Crossref, Google Scholar
• [30] Kamada Y, Kojima F (2015) Efficient matching under distributional constraints: Theory and applications. Amer. Econom. Rev. 105(1):67–99.Crossref, Google Scholar
• [31] Kamada Y, Kojima F (2017) Stability concepts in matching with distributional constraints. J. Econom. Theory 168:107–142.Crossref, Google Scholar
• [32] Kamada Y, Kojima F (2018) Stability and strategy-proofness for matching with constraints: A necessary and sufficient condition. Theoret. Econom. 13(2):761–794.Crossref, Google Scholar
• [33] Kamada Y, Kojima F (2020) Accommodating various policy goals in matching with constraints. Japanese Econom. Rev. 71(1):101–133.Crossref, Google Scholar
• [34] Kelso AS, Crawford VP (1982) Job matching, coalition formation, and gross substitutes. Econometrica 50(6):1483–1504.Crossref, Google Scholar
• [35] Kojima F, Sun N, Yu NN (2020) Job matching under constraints. Amer. Econom. Rev. 110(9):2935–2947.Crossref, Google Scholar
• [36] Kojima F, Sun N, Yu NN (2023) Job matching with subsidy and taxation. Rev. Econom. Stud. 91(1):372–402.Crossref, Google Scholar
• [37] Kojima F, Tamura A, Yokoo M (2018) Designing matching mechanisms under constraints: An approach from discrete convex analysis. J. Econom. Theory 176:803–833.Crossref, Google Scholar
• [38] Kreps DM (2023) Microeconomic Foundations I: Choice and Competitive Markets, vol. 1 (Princeton University Press, Princeton, NJ).Google Scholar
• [39] Kumano T, Kurino M (2026) Quota adjustment process. Amer. Econom. Rev. Forthcoming.Google Scholar
• [40] Kushnir AI, Lokutsievskiy LV (2021) When is a monotone function cyclically monotone? Theoret. Econom. 16(3):853–879.Crossref, Google Scholar
• [41] Markovits D (2019) The Meritocracy Trap: How America’s Foundational Myth Feeds Inequality, Dismantles the Middle Class, and Devours the Elite (Penguin UK, New York).Google Scholar
• [42] Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic Theory (Oxford University Press, New York).Google Scholar
• [43] Murota K (2003) Discrete Convex Analysis (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• [44] Murota K (2016) Discrete convex analysis: A tool for economics and game theory. J. Mechanism Institution Design 1(1):151–273.Crossref, Google Scholar
• [45] Murota K, Shioura A (2003) Quasi M-convex and L-convex functions—Quasiconvexity in discrete optimization. Discrete Appl. Math. 131(2):467–494.Crossref, Google Scholar
• [46] Murota K, Shioura A (2018) Simpler exchange axioms for M-concave functions on generalized polymatroids. Japanese J. Indust. Appl. Math. 35(1):235–259.Crossref, Google Scholar
• [47] Murota K, Yokoi Y (2015) On the lattice structure of stable allocations in two-sided discrete-concave market. Math. Oper. Res. 40(2):460–473.Link, Google Scholar
• [48] Oxley JG (2006) Matroid Theory, vol. 3 (Oxford University Press, Oxford, UK).Google Scholar
• [49] Paes Leme R (2017) Gross substitutability: An algorithmic survey. Games Econom. Behav. 106:294–316.Crossref, Google Scholar
• [50] Plott CR (1973) Path independence, rationality, and social choice. Econometrica 41(6):1075–1091.Crossref, Google Scholar
• [51] Roth AE (1984) Stability and polarization of interests in job matching. Econometrica 52(1):47–58.Crossref, Google Scholar
• [52] Sönmez T, Yenmez MB (2022) Affirmative action in India via vertical, horizontal, and overlapping reservations. Econometrica 90(3):1143–1176.Crossref, Google Scholar
• [53] Sowell T (2004) Affirmative Action Around the World: An Empirical Study (Yale University Press, New Haven, CT).Google Scholar
• [54] Yokoi Y (2019) Matroidal choice functions. SIAM J. Discrete Math. 33(3):1712–1724.Crossref, Google Scholar
• [55] Yokote K, Hafalir IE, Kojima F, Yenmez MB (2023) Rationalizing path-independent choice rules. Preprint, submitted March 2, https://arxiv.org/abs/2303.00892.Google Scholar