Paula Jaramillo

Asymmetrically Fair Rules for an Indivisible Good Problem with a Budget Constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.

Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare ✩

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.

Minimal Consistent Enlargements of the Immediate Acceptance Rule and the Top Trading Cycles Rule in School Choice

We consider school choice problems. We are interested in solutions that satisfy consistency. Consider a problem and a recommendation made by the solution for the problem. Suppose some students are removed with their positions in schools. Consider the “reduced” problem consisting of the remaining students and the remaining positions. Consistency states that in the reduced problem, the solution should assign each remaining student to the same school as initially. Neither the immediate acceptance rule (also known as the Boston mechanism) nor the top trading cycles rules is consistent. We show that the Pareto solution is the smallest consistent solution containing the immediate acceptance rule. It is also the smallest consistent solution containing the top trading cycles rule.

Congestion in Irrigation Problems (Congestion en problems de irrigacion)

Consider a problem in which the cost of building an irrigation canal has to be divided among a set of people. Each person has different needs. When the needs of two or more people overlap, there is congestion. In problems without congestion, a unique canal serves all the people and it is enough to finance the cost of the largest need to accommodate all the other needs. In contrast, when congestion is considered, more than one canal might need to be built and each canal has to be financed.In problems without congestion, axioms related with fairness (equal treatment of equals) and group participation constraints (no-subsidy or core constraints) are compatible. With congestion, we show that these two axioms are incompatible.We define weaker axioms of fairness (equal treatment of equals per canal) and group participation constraints (no-subsidy across canals). These axioms in conjunction with a solidarity axiom (congestion monotonicity) and another axiom (independence of at-least-as-large-length) characterize the sequential weighted contribution family. Moreover, when we include a stronger version of congestion monotonicity and other axioms, we characterize subfamilies of these rules.