Closest Types: A Simple non-Zone-Based Framework for School Choice (2013-01). My proposal for how to reform choice menus in school choice in Boston. The current framework is to divide the city into zones. But zones have unnatural boudary lines and are difficult to revise to adapt to future changes (because those living on the boundary will be significantly affected.) Instead, we allow every student to choose from the any close-to-home school (within say x miles), the 2 closest Top 25% school, the 4 closest top 50% school, the 6 closest top 75% school and the 3 closest capacity school. This provides quality and capacity guarantees in menu and can straightforwardly adapt to any quality metric, changes in quality, or changes in demographics. See write-up for details.
Correcting Finite Sample Biases in Conventional Estimates of Power Variation and Jumps(2009-04). In many current financial time-series models, especially jump detection tests, researchers use estimators such as bi-power variation, tri-power quarticity, or quad-power quarticity. It turns out that in the presence of the daily U-shaped pattern in volatility (higher volatility in the beginning and end of trading day), these estimators estimators are significantly downward bias under finite interval sampling. This distorts the statistics of various jump testss. This paper seeks to design estimators that correct for this bias, and in the process bias-adjusting currently used jump tests.
A simple result relating socially concave games to Rosen's convergence condition(2009-03). In [Even-dal et. al. '09], they show that for a class of games called "socially concave games," when players use no-regret policies, their average strategies converge to a epsilon-Nash equilibrium. Our simple result shows that in strict socially concave games, under no-regret policies, the strategies themselves converge to a Nash-equilibrium, using a condition due to Rosen ([Rosen '65]). Hence, in this subclass of socially concave games, we show a stronger result. I also wrote a summary of what is known and not known in this topic.
MegaTorrent: An Incentive-Based Solution to Freeriding in P2P File-Sharing Networks(2008-04) (with Kshipra Bhawalkar). A paper about using a Pagerank-like reputation system to make P2P file sharing systems incentive compatible (encourage contribution instead of free-riding). Currently BitTorrent's "optimistic unchoking" allows users to download without uploading. We tackle this by making agents' download speed dependent on their "Eigenscore," which they can only improve by helping other reputable users download.