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A new perspective on Kesten’s school choice with consent idea.(English)Zbl 1309.91103

Summary: We revisit the school choice problem with consent proposed byO. Kesten [Q. J. Econ. 125, No. 3, 1297–1348 (2010;Zbl 1197.91153)], which seeks to improve the efficiency of the student-optimal deferred acceptance algorithm (DA) by obtaining students’ consent to give up their priorities. We observe that for students to consent, we should use their consent only when their assignments are Pareto unimprovable. Inspired by this perspective, we propose a new algorithm which iteratively reruns DA after removing students who have been matched with underdemanded schools, together with their assignments. While this algorithm is outcome equivalent to Kesten’s EADAM, it is more accessible to practitioners due to its computational simplicity and transparency on consenting incentives. We also adapt this algorithm for school choice problems with weak priorities to simplify the stable improvement cycles algorithm proposed byA. Erdil andH. Ergin [“What’s the matter with tie-breaking? Improving efficiency in school choice”, Amer. Econ. Rev. 98, No. 3, 669–689 (2008;doi:10.1257/aer.98.3.669)].

MSC:

91B68 Matching models

Citations:

Zbl 1197.91153

Cite

References:

[1]Abdulkadiroğlu, A.; Sönmez, T., School choice: a mechanism design approach, Amer. Econ. Rev., 93, 729-747 (2003)
[2]Abdulkadiroğlu, A.; Pathak, P.; Roth, A., Strategy-proofness versus efficiency in matching with indifferences: redesigning the NYC high-school match, Amer. Econ. Rev., 99, 1954-1978 (2009)
[3]Balinski, M.; Sönmez, T., A tale of two mechanisms: student placement, J. Econ. Theory, 84, 73-94 (1999) ·Zbl 0916.90008
[4]Bando, K., On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm, Games Econ. Behav., 87, 269-287 (2014) ·Zbl 1302.91153
[6]Dubins, L.; Freedman, D., Machiavelli and the Gale-Shapley algorithm, Amer. Math. Mon., 88, 485-494 (1981) ·Zbl 0449.92024
[7]Erdil, A., Strategy-proof stochastic assignment, J. Econ. Theory, 151, 146-162 (2014) ·Zbl 1296.91174
[8]Erdil, A.; Ergin, H., What’s the matter with tie-breaking? Improving efficiency in school choice, Amer. Econ. Rev., 98, 669-689 (2008)
[9]Ergin, H., Efficient resource allocation on the basis of priorities, Econometrica, 70, 2489-2497 (2002) ·Zbl 1141.91563
[10]Gale, D.; Shapley, L., College admissions and the stability of marriage, Amer. Math. Mon., 69, 9-15 (1962) ·Zbl 0109.24403
[11]Kesten, O., On two competing mechanisms for priority-based allocation problems, J. Econ. Theory, 127, 155-171 (2006) ·Zbl 1125.91019
[12]Kesten, O., School choice with consent, Quart. J. Econ., 125, 1297-1348 (2010) ·Zbl 1197.91153
[14]Kojima, F.; Manea, M., Axioms for deferred acceptance, Econometrica, 78, 633-653 (2010) ·Zbl 1229.91246
[15]Roth, A., The economics of matching: stability and incentives, Mathematics Operations Res., 7, 617-628 (1982) ·Zbl 0496.90008
[16]Shapley, L.; Scarf, H., On cores and indivisibility, J. Math. Econ., 1, 23-37 (1974) ·Zbl 0281.90014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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