[1] Abdulkadiroˇglu, A., Pathak, P. A., and Roth, A. E. The New York City high school match. American Economic Review, Papers and Proceedings, 95 (2):364–367, 2005.
[2] Abdulkadiroˇglu, A. and Sönmez, T. House allocation with existing tenants. Journal of Economic Theory, 88(2):233–260, 1999.
[3] Abdulkadiroˇglu, A. and Sönmez, T. School choice: A mechanism design approach. American Economic Review, 93(3):729–747, 2003.
[4] Afacan, M. O., Bó, I., and Turhan B. Assignment maximization. Working paper arXiv e-prints, arXiv-2012, 2020.
[5] Andersson, T. and Ehlers, L. Assigning refugees to landlords in sweden: Efficient, stable, and maximum matchings. The Scandinavian Journal of Economics, 122(3):937–965, 2020.
[6] Andersson, T., Ehlers, L., and Martinello, A. Dynamic refugee matching. Cahier de recherche, 2018-10.
[7] Grandoni, F. andKrysta, P. and Leonardi, S. andVentre, C. Utilitarian mechanism design for multiobjective optimization. SIAM Journal on Computing, 43(4):1263–1290, 2014.
[8] Arnosti, N. and Shi, P. Design of lotteries and wait-lists for affordable housing allocation. Management Science, 2020.
[9] Balinski, M. and Sönmez, T. Tale of two mechanisms: student placement. Journal of Economic theory, 84(1):73–94, 1999.
[10] Biró, P., Fleiner, T., Irving, R. W., and Manlove, D. F. The college admissions problem with lower and common quotas. Theoretical Computer Science 411, (34-36):3136–3153, 2010.
[11] Bloch, F. and Cantala, D. Dynamic assignment of objects to queuing agents. American Economic Journal: Microeconomics, 9(1):88–122, 2017.
[12] Braun, S., Dwenger, N., Kübler, D., and Westkamp, A. Implementing quotas in university admissions: An experimental analysis. Games and Economic Behavior, 85:232–251, 2014.
[13] Cantala, D. and Pápai, S. Reasonably and securely stable matching. Tech. rep, 2014.
[14] Cormen, T. H., Leiserson, C.E., Rivest, R. L., and Stein, C. Section 26.2: The ford–fulkerson method. Introduction to Algorithms (Second ed.), ISBN 0-262-03293-7:651–664, 2001.
[15] Damiano, E. and Lam, R. Stability in dynamic matching markets. Games and Economic Behavior, 52(1):34–53, 2005.
[16] Doval, L. Dynamically stable matching. Available at SSRN 3411717, 2019.
[17] Du, S. and Livne, Y. Rigidity of transfers and unraveling in matching markets. Available at SSRN 2203910, 2014.
[18] Dubins, L. E. and Freedman, D. Machiavelli and the Gale-Shapley algorithm. Mathematical Monthly, 88(7):485–494, 1981.
[19] Dworczak, P. Deferred acceptance with compensation chains. Operations Research, 69(2):456–468, 2021.
[20] Ehlers, L., Hafalir, I. E., Yenmez, M. B., and Yildirim, M. A. School choice with controlled choice constraints: Hard bounds versus soft bounds. Journal of Economic Theory, (153):648–683, 2014.
[21] Erdil, A. and Ergin, H. I. What’s the matter with tie-breaking? improving efficiency in school choice. American Economic Review, 98(3):669–689, 2008.
[22] Ergin, H. I. Efficient resource allocation on the basis of priorities. Econometrica, 70(6):2489–2497, 2002.
[23] Fragiadakis, D. and Troyan, P. Improving matching under hard distributional constraints. Theoretical Economics, (12):863–908, 2017.
[24] Fragiadakis, D., Troyan, P., Iwasaki, A., Ueda, S., and Yokoo, M. Strategyproof matching with minimum quotas. ACM Transactions on Economics and Computation, 4(1):Article 6, 2015.
[25] Gale, D. and Shapley, L. S. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9–15, 1962.
[26] Hafalir, I. E., Yenmez, M. B., and Yildirim, M. A. Effective affirmative action in school choice. Theoretical Economics, 8(2):325–363, 2013.
[27] Hall, P. On representatives of subsets. Journal of the London Mathematical Society, 1:26–30, 1935.
[28] Hamada, K., Iwama, K., and Miyazaki, S. The hospitals/residents problem with lower quotas. Algorithmica, 74(1):440–465, 2016.
[29] Hatfield, J. W. and Milgrom, P. R. Matching with contracts. American Economic Review, 95(4):913–935, 2005.
[30] Herrnstein, R. J. Relative and absolute strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4(3):267, 1961.
[31] Hopcroft, J. E. and Karp, R. M. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2:225–231, 1973.
[32] Irving, R. W., Kavitha, T., Mehlhorn, K., Michail, D., and Paluch, K. Rank-maximal matchings. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete Algorithms, pages 68–75, 2006.
[33] Kahn, A. B. Topological sorting of large networks. Communications of the ACM, 5(11):558–562, 1962.
[34] Kamada, Y. and Kojima, F. Efficient matching under distributional constraints: Theory and applications. American Economic Review, 105(1):67–99, 2015.
[35] Kamada, Y. and Kojima, F. Fair matching under constraints: Theory and applications. Review of Economic Studies, 2018.
[36] Kawagoe, T. and T. Matsubae. Matching with minimal quota: A case study of the japanese university student-supervisor assignment. Available at SSRN 3429626, 2017.
[37] Kelso Jr, A. S. and Crawford, V. P. Job matching, coalition formation, and gross substitutes. Econometrica, pages 1483–1504, 1982.
[38] Kesten, O. Student placement to public schools in the us: Two new solutions. Working paper, University of Rochester, 2004.
[39] Kesten, O. On two competing mechanisms for priority-based allocation problems. Journal of Economic Theory, 127(1):155–171, 2006.
[40] Kesten, O. School choice with consent. The Quarterly Journal of Economics, 125:3, 2010.
[41] Klijn, F., Pais, J., and Vorsatz, M. Static versus dynamic deferred acceptance in school choice: Theory and experiment. Games and Economic Behavior, 113:147–163, 2019.
[42] Kojima, F. School choice: Impossibilities for affirmative action. Games and Economic Behavior, 75(2):685–693, 2012.
[43] Kominers, S. D. and Sönmez, T. Matching with slot-specific priorities: Theory. Theoretical Economics, 11(2):683–710, 2016.
[44] Kotowski, M. H. A perfectly robust approach to multiperiod matching problems. 2019.
[45] Kurino, M. Credibility, efficiency, and stability: A theory of dynamic matching markets. The Japanese Economic Review, 71(1):135–165, 2020.
[46] Kuvalekar, A. A fair procedure in a marriage market. Available at SSRN 2688630, 2014.
[47] Li, S. Obviously strategy-proof mechanisms. American Economic Review, 107(11):3257–87, 2017.
[48] Liu, C. Stability in repeated matching markets. arXiv preprint arXiv:2007, 03794, 2020.
[49] Martínez, R., Massó, J., Neme, A., and Oviedo, J. Single agents and the set of manyto-one stable matchings. Journal of Economic Theory, 91(1):91–105, 2000.
[50] Morrill, T. Making efficient school assignment fairer. Working paper, North Carolina State University.[1311], 2013.
[51] Pápai, S. Strategyproof assignment by hierarchical exchange. Econometrica, 63(6):1403–1433, 2000.
[52] Pápai, S. Strategyproof and nonbossy multiple assignments. Journal of Public Economic Theory, 3:257–271, 2001.
[53] Pápai, S. Matching with minimal priority rights. Working paper, Concordia University, 2013.
[54] Pereyra, J. S. A dynamic school choice model. Games and Economic Behavior, 80:100–114, 2013.
[55] Pycia, M. and Ünver, M. U. Incentive compatible allocation and exchange of discrete resources. Theoretical Economics, 12:287–329, 2017.
[56] Romero-Medina, A. Equitable selection in bilateral matching markets. Theory and Decision, 58(3):305–324, 2005.
[57] Romero-Medina, A. and Kuvalekar, A. V. A fair procedure in a marriage market. Universidad Carlos III de Madrid. Departamento de Economía, (31711), 2021.
[58] Roth, A. E. The economics of matching: Stability and incentives. Mathematics of Operations Research, 7(4):617–628, 1982.
[59] Roth, A. E. The evolution of the labor market for medical interns and residents: a case study in game theory. Journal of Political Economy, 92(6):991–1016, 1984.
[60] Roth, A. E. On the allocation of residents to rural hospitals: a general property of two-sided matching markets. Econometrica, 1:425–427, 1986.
[61] Roth, A. E. The economist as engineer: Game theory, experimentation, and computation as tools for design economics. Econometrica, 70:1341–1378, 2002.
[62] Roth, A. E. Who gets what—and why: The new economics of matchmaking and market design. Houghton Mifflin Harcourt, 2015.
[63] Roth, A. E. and Peranson, E. The redesign of the matching market for American physicians: Some engineering aspects of economic design. American Economic Review, 89(4):748–780, 1999.
[64] Roth, A. E. and Sotomayor, M. Two-sided matching. Handbook of game theory with economic applications, 1:485–541, 1992.
[65] Roth, A. E., Sönmez, T., and Ünver, M. U. Kidney exchange. The Quarterly Journal of Economics, 119(2):457–4881, 2004.
[66] Satterthwaite M. and Sonnenschein H. Strategy-proof allocation mechanism at differentiable points. Review of Economic Studies, XL VIII:587–597, 1981.
[67] Shapley, L. S. and Scarf, H. On cores and indivisibility. Journal of Mathematical Economics, 1(23), 1974.
[68] Shapley, L. S. and Shubik, M. The assignment game I: The core. International Journal of Game Theory, 1(1):111–130, 1971.
[69] Svensson, L-G. Queue allocation of indivisible goods. Social Choice and Welfare, 11:323–330, 1994.
[70] Svensson, L-G. Strategy-proof allocation of indivisible goods. Social Choice and Welfare, 16:557–567, 1999.
[71] Teo, C. P. and Sethuraman, J. The geometry of fractional stable matchings and its applications. Mathematics of Operations Research, 23(4):874–891, 1998.
[72] Tomoeda, K. Finding a stable matching under type-specific minimum quotas. Journal of Economic Theory 176, page 81–117, 2017.
[73] Troyan, P. and Morrill, T. Obvious manipulations. Journal of Economic Theory, 85:104970, 2020.
[74] Westkamp, A. An analysis of the german university admissions system. Economic Theory, 53(3):561–589, 2013.
[75] Yahiro, K., Barrot, N. Zhang, Y., and Yokoo, M. Strategyproof and fair matching mechanism for ratio constraints. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, 53(3):59–67, 2018.