Research

In fair division of indivisible items, domain restriction has played a key role in escaping from negative results and providing structural insights into the computational and axiomatic boundaries of fairness. One notable subdomain of additive preferences, the lexicographic domain, has yielded several positive results in dealing with goods, chores, and mixtures thereof. However, the majority of work within this domain primarily consider strict linear orders over items, which do not allow the modeling of more expressive preferences that contain indifferences (ties). We investigate the most prominent fairness notions of envy-freeness up to any (EFX) or some (EF1) item under weakly lexicographic preferences. For the goods-only setting, we develop an algorithm that can be customized to guarantee EF1, EFX, maximin share (MMS), or a combination thereof, along the efficiency notion of Pareto optimality (PO). From the conceptual perspective, we propose techniques such as preference graphs and potential envy that are independently of interest when dealing with ties. Finally, we demonstrate challenges in dealing with chores and highlight key algorithmic and axiomatic differences of finding EFX solutions with the goods-only setting. Nevertheless, we provide the first algorithm that guarantees an EF1 and PO allocation for the weakly-lexicographic chores-only instances.

We study the fair allocation of mixtures of indivisible goods and chores under lexicographic preferences—a subdomain of additive preferences. A prominent fairness notion for allocating indivisible items is envy-freeness up to any item (EFX). Yet, its existence and computation has remained a notable open problem. By identifying a class of instances with terrible chores, we show that determining the existence of an EFX allocation is a computationally hard problem. This result immediately implies the intractability of EFX under additive preferences. Nonetheless, we propose a natural subclass of lexicographic preferences for which an EFX and Pareto optimal (PO) allocation is guaranteed to exist and can be computed efficiently. Focusing on two weaker fairness notions, we investigate finding EF1 and PO allocations for special instances with terrible chores and show that MMS and PO allocations can be computed efficiently for any mixed instance with lexicographic preferences.

In school choice, families often face uncertainty about their preferences or admission probabilities, which highlights the importance of information design. By strategically providing information, designers can guide families to make more informed decisions for students, enhancing the overall efficiency and fairness of the school choice process. In this study, we introduce a novel model for school choice where students do not fully know their preferences and have prior beliefs about their school options. Our work identifies the optimal information structure to maximize students' welfare when the assignment algorithm is the celebrated Deferred Acceptance. We demonstrate that this optimal structure not only recommends a school to each student but also discloses all viable choices at the decision point. Additionally, we show that for each school, there is a pivotal student who is recommended to select that school. Our approach combines analytical techniques using linear programming with computational methods employing Gurobi to derive and implement optimal solutions. This interdisciplinary approach, in turn, allows us to provide actionable insights into information disclosure policies that can improve decision-making in school admissions.

This project involves the manipulation and analysis of extensive datasets to estimate student preferences for universities. Over a span of nearly 15 years, these datasets contain a wealth of information, including students' central exam scores, rank-order lists of preferred universities, and demographic details such as household information and parental wages. Cleaning these datasets necessitated attention to detail, especially in addressing missing values such as proximity to universities. Leveraging zip code information for households, we computed average distances to fill in missing data points. We applied big data techniques, particularly multinomial regression to predict student preferences, leading to the development and analysis of a comprehensive model. The primary objective of this research was to discern the policy implications of the existing educational system. Our findings emphasized the imperative for targeted policies, particularly to support students in rural areas and the implementation of gender-based initiatives.

In this paper, we give a novel characterization of Nash implementability of social choice rules in the presence of at least three agents by weakening the notion of neutrality in a suitable manner. Maskin [1977] defined a notion of monotonicity for social choice rules – referred to as Maskin monotonicity since then – and showed that it was necessary for Nash implementability. As this kind of monotonicity was not sufficient for Nash implementability, Maskin monotonicity was conjoined with other conditions imposed upon social choice rules, the satisfaction of which would render them Nash-implementable. No veto power and neutrality, none of which is necessary for Nash implementability, constitute the two main examples of such additional conditions. A full characterization of Nash implementability was then obtained by Moore and Repullo [1990] via a suitably weakened version of no veto power and Maskin monotonicity in the presence of at least three agents. These two conditions were merged by Danilov [1992] into a single kind of monotonicity, referred to as essential monotonicity. We ascribe the role of no veto power above to neutrality, and define a weak kind of neutrality. The main tool that we use in doing so is the notion of a critical profile introduced by Koray et al. [2001] and essentially require that the neutrality condition is satisfied by the restriction of a social choice rule to its critical profiles. Referring to this weakened form of neutrality as critical neutrality, we show that the conjunction of Maskin monotonicity and critical neutrality is equivalent to Nash implementability when there are at least three agents.

• Asian School in Economic Theory by The Econometric Society, NYU, Abu Dhabi, UAE, 2025

• Price Theory Summer Camp, Becker Friedman Institute at UChicago, Chicago, US, 2024.

• Report Author, The 4th annual ACM SIGecom Winter Meeting, 2024

• Presenter, The 32nd IJCAI, Macao, S.A.R, 2023.

• Presenter, Summer School on Computational Social Choice, UvA, AMS, Netherlands, 2023

• Presenter, Pennsylvania Economic Theory Conference, PSU, State College, US, 2023.

• Discussant, The 39th Bosphorus Workshop on Economic Design, Bodrum, Türkiye, 2019.

• Presenter, Workshop on Fundamentals of Trading, SSE, Riga, Latvia, 2017.