**Working Papers

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**When does an additional stage improve welfare in centralized assignment?**(w/ M. B. Yenmez). [ssrn] [repec]

We study multistage centralized assignments to allocate scarce resources based on priorities in the context of school choice. We characterize the capacity-priority profiles of schools under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage enrollment system to the truthful equilibrium outcome of the 1-stage enrollment system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage enrollment system may Pareto dominate the truthful equilibrium outcome of the 1-stage enrollment system.

**Unified versus divided enrollment in school choice: improving student welfare in Chicago**(w/ M. B. Yenmez). [ssrn] [repec]

The Chicago Board of Education is implementing a centralized clearinghouse to assign students to schools for 2018-19 admissions. In this clearinghouse, each student can simultaneously be admitted to a selective and a nonselective school. We study this divided enrollment system and show that an alternative unified enrollment system, which elicits the preferences of students over all schools and assigns each student to only one school, is better for students when choice rules of schools are substitutable. Furthermore, we characterize the sources of inefficiency in the divided system.

In several matching markets, in order to achieve diversity, agents' priorities are allowed to vary across an institution’s available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a lexicographic choice rule. Lexicographic choice rules have been particularly useful in achieving diversity at schools while allocating school seats. We provide a characterization of lexicographic choice rules, which reveals their distinguishing properties from other plausible choice rules. Moreover, we study the market design implications of using lexicographic choice rules and provide a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure. We also discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.

We show that there is no consistent Pareto improvement over any stable mechanism. To overcome this impossibility, we introduce the following weak consistency requirement: Whenever a set of students, each of whom is assigned to a school that is under-demanded at the student-optimal stable matching, are removed with their assigned seats, then the assignments of the remaining students should not change. We show that EADA (Kesten, 2010) is the unique mechanism that is weakly consistent and Pareto improves over the student-optimal stable mechanism.

**On acceptant and substitutable choice rules**(w/ S. Dogan and K. Yildiz). [ssrn]

*Mathematics of Operations Research, revision requested.*

Each

*acceptant*and*substitutable*choice rule is known to have a*maximizer-collecting*representation: there exists a list of priority orderings such that from each choice set that includes more elements than the capacity, the choice is the union of the priority orderings' maximizers (Aizerman and Malishevski, 1981). We introduce the notion of a*prime atom*and constructively prove that the number of prime atoms of a choice rule determines its smallest size maximizer-collecting representation. We show that responsive choice rules require the maximal number of priority orderings in their maximizer-collecting representations among all acceptant and substitutable choice rules. We characterize maximizer-collecting choice rules in which the number of priorities equals the capacity. We also show that if the capacity is greater than three and the number of elements exceeds the capacity by at least two, then no acceptant and substitutable choice rule has a maximizer-collecting representation of the size equal to the capacity.## Published Papers

Object allocation via immediate acceptance: characterizations and an affirmative action application (w/ B. Klaus). [repec] [publisher]

*Journal of Mathematical Economics, 79, 140-156, 2018.*A new ex-ante efficiency criterion and implications for the probabilistic serial mechanism (w/ S. Dogan and K. Yildiz). [ssrn] [publisher]

*Journal of Economic Theory,**175, 178-200, 2018.*Eliciting the socially optimal allocation from responsible agents. [ssrn] [publisher]

*Journal of Mathematical Economics, 73, 103-110, 2017.*Stability and the immediate acceptance rule when school priorities are weak

**(w/ W. J. Cho). [ssrn] [publisher]***International Journal of Game Theory, 46, 991-1014, 2017.*How to control controlled school choice: comment [ssrn] [repec] [publisher]

*American Economic Review, 107, 1362-64, 2017.*Responsive affirmative action in school choice. [ssrn] [repec] [publisher]

*Journal of Economic Theory, 165, 69-105, 2016.*Nash-implementation of the no-envy solution on symmetric domains of economies. [ssrn] [publisher]

*Games and Economic Behavior, 98, 165-171, 2016.*Equivalence of efficiency notions for ordinal assignment problems (w/ W. J. Cho). [ssrn] [publisher] [online appendix]

*Economics Letters, 46, 8-12, 2016.*Efficiency and stability of probabilistic assignments in marriage problems (w/ K. Yildiz). [ssrn] [publisher]

*Games and Economic Behavior, 95, 47-58, 2016.*Maskin-monotonic scoring rules (w/ S. Koray). [publisher]

*Social Choice and Welfare, 44, 423-432, 2015.*