We study the assignment of middle-school students to high schools in China. In an attempt to provide wider access to quality education for students from underperforming middle-schools, a series of affirmative action reforms have been implemented throughout China in the last decade. Under these reforms, each high school sets aside a specific privilege quota for certain middle schools. A student who receives this privilege obtains a lump-sum of extra points in the entrance exam. We show that the existing implementation of these reforms serve little toward the intended objectives. A major difficulty lies in determining which students should be granted the privilege a priori. We propose a choice function that ``endogenously'' determines students privileges. The cumulative offer mechanism associated with this choice function is stable, strategy-proof and is essentially unique among those that provide individual rationality, nonwastefulness and elimination of justified envy suitably defined for this context. Empirical analysis quantify the gains from our proposal relative to the current mechanisms.

Judicial systems around the world widely differ in the degree they allow litigants to exercise their right to legal counsel. When litigants are completely free to choose their lawyers and vice versa, blocking pairs between litigants and lawyers must be eliminated leading to stable matchings. In this context, a negative externality arises: a pairing between a stronger lawyer and a litigant conflicts with the interests of the opposing litigant and his lawyer. We characterize conditions under which realized matchings can be rationalized as stable. We show that stable matchings always lead to negatively assortative lawyer pairings, i.e., at any stable matching, strong lawyers face weak opponents. Stable matchings are always efficient, but may not belong to the core.

A multitude of systems are in place throughout Europe for the assignment of lawyers to indigent litigants. However, the repetitive nature of the problem leads to serious congestion issues. We formulate this issue as a market design problem and propose a class of efficient and incentive compatible mechanisms.

This paper proposes two mechanisms that aim to improve Deferred Acceptance (DA) mechanism, namely, the Protecting Line Control Mechanism (PLCM) and the Protecting Line Re-submission Mechanism (PLRM). Theory has shown that no strategyproof mechanism Pareto dominates DA, which will get the best matching for each student among all the stable matchings. Neither of the two mechanisms proposed by this paper are not strategyproof, but both are strategyproof in the large and Pareto dominates DA.
In both the mechanisms, after students submit their rank order lists (ROLs), we run a DA base on which we identify the lowest priority score required to get into each school. Both mechanisms work as if students are trading their DA assignments for some schools they prefer more. However, unlike the Top Trading Cycle (TTC), in the mechanisms I propose, one can only trade her DA assignments for another school when she is above/below the cutoff line. I show that by allowing such trades to take place, both mechanisms Pareto dominate DA. However, due to the constraints of the cutoff lines, they may also lose efficiency.
I show that for both mechanisms, if the cutoff lines are treated as exogenous, i.e., if no single individual can change the cutoff line of any school by unanimously misrepresenting her preference, then both mechanisms are strategyproof. That is, both mechanisms are strategyproof in the large. I also show that both mechanisms improve DA but at the cost of stability to some degree