I am a senior researcher in the theory group in Microsoft Research, Redmond.
I am interested in what I call Automated Economics, which studies the question of how technology can be used to improve the efficiency of economic systems. My other interest is in Algorithms: I am interested in designing algorithms that are faster, simpler, work online or in a distributed fashion, for some of the basic combinatorial optimization problems.
Mentees (Interns and Postdocs)
- Ben Birnbaum, Flatiron Healrh
- Balu Sivan, Google Research
- Zhiyi Huang, University of Hong Kong
- Jamie Morgenstern, University of Pennsylvania
- Janardhan Kulkarni, Microsoft Research
- Alex Psomas, UC Berkeley
- A new auction format for IPL players auctions [pdf].
- New Convex Programs for Fisher’s Market Model and its Generalizations [arXiv pdf] with Kamal Jain, Tung Mai, Vijay V. Vazirani and Sadra Yazdanbod.
- We present the following results pertaining to Fisher’s market model:
- We give two natural generalizations of Fisher’s market model: In model M_1, sellers can declare an upper bound on the money they wish to earn (and take back their unsold good), and in model M_2, buyers can declare an upper bound on the amount to utility they wish to derive (and take back the unused part of their money).
- We derive convex programs for the linear case of these two models by generalizing a convex program due to Shmyrev and the Eisenberg-Gale program, respectively.
- We generalize the Arrow-Hurwicz theorem to the linear case of these two models, hence deriving alternate convex programs.
- For the special class of convex programs having convex objective functions and linear constraints, we derive a simple set of rules for constructing the dual program (as simple as obtaining the dual of an LP). Using these rules we show a formal relationship between the two seemingly different convex programs for linear Fisher markets, due to Eisenberg-Gale and Shmyrev; the duals of these are the same, up to a change of variables.