Research

Monitoring Costs and the Management of Common-Pool-Resources (Job Market Paper, In Progress)

Abstract. I lay down a simple model of a fishery and analyze outcomes of a cap-and-trade program when monitoring/quota enforcement is costly and imperfect. I highlight the possibility of stable low-stock equilibria which I have not yet seen in the literature. Nonetheless, I list some good reasons to focus on the high-stock equilibria and compare different mechanisms for monitoring. Voluntary contribution mechanisms lead to classic free-riding problems where only agents of the most productive type contribute anything to monitoring; while I have no theorems for the case where agents vote over monitoring contributions, my numerical exercises indicate that a median-voter theorem applies, where the ideal monitoring level of the type of median-productivity is chosen. Finally, I intend to compare that with the case where there is a tax on quota, and the revenues from that tax fund the monitoring effort. Even though this comparison is useful in itself, I intend to use it as a platform for more general results, where the regulator uses the cap and quota endowments to achieve the multiple goals of efficiency, voluntary participation and stock preservation.

Combinatorial Assignment Under Dichotomous Preferences (Working Paper)

Abstract. We consider the problem of assigning shares of a imperfectly divisible resource when pref- erences are dichotomous. One such problem is the problem of assigning bundles from a finite set of indivisible objects to a finite set of agents. When preferences are dichotomous, mech- anisms that satisfy voluntary participation only require agents to report a set of acceptable bundles/shares. We characterize strategyproof mechanisms for such problems and provide a mechanism that is utilitarian-efficient, strategyproof and envy-free, thereby showing that impossibilities like the ones pointed out by Kojima (2009) can be circumvented if we assume dichotomous preferences. We also show that, unlike in the assignment problem with dichoto- mous preferences of Bogomolnaia and Moulin (2004), the existence of a Lorenz-dominant assignment is not guaranteed. We analyze real-world difficulties involved in using efficient mechanisms, both from a computational and a strategic point of view. In particular, we show that utilitarian-efficient mechanisms require computations that can have running times that are exponentially long in the number of agents, but we point out that some classes of problems can be solved faster. We also show that agents with general preferences facing a mechanism that is strategyproof and efficient in the dichotomous domain might have an incentive to mis- report their acceptable shares/bundles, and in that case, the only profitable deviation is to report a smaller set of acceptable shares/bundles. PDF, Sources.

Teaching

I have taught the Mathcamp at the Division of the Humanities and Social Sciences at Caltech. The course reviews some of the he most useful mathematical tools for the first-year PhD students at the division. Check the Syllabus, some code for computational sessions in the lab, and, most important, the problem set.

I was the TA for an undergraduate course in Power Systems at Caltech. I wrote some quick-and-dirty notes on the basics of convex optimization and Karush-Kuhn-Tucker conditions. They are not very polished, but they are a good complement to more rigorous texts (mentioned in the final section), providing intuition and some useful hints.

I have worked as a volunteer tutor for School On Wheels, an NGO that provides one-one-one tutoring assistance for homeless children. If you believe that education is the way to provide opportunity to everyone, check them out! You can help in many ways: tutoring and donating are just two out of many options. For example, besides my tutoring activity, I also participated on a workshop where we discussed different issues in the education of homeless children. I talked about how to enrich the solution of math problems with an inquisitive trial-and-error approach. Here are the slides of the talk. And here is a pretty multiplication table that you can use to teach not only multiplication, but also some good principles of graphics/information design and table layout!

I am always happy to discuss ideas for improving education at all levels. A sample of topics on education that have recently caught my attention are: evaluation methods that give good feedback to our students and encourage learning; ways of using measurements, experiments and computation to aid middle and high-school students' understanding of mathematical concepts; and a curriculum for economics majors in college.