Optimal Dynamic Auctions, 2008, with Mallesh Pai.

We consider a dynamic auction problem motivated by the traditional single-leg, multi-period revenue management problem. A seller with C units to sell faces potential buyers with unit demand who arrive and depart over the course of T time periods. The time at which a buyer arrives, her value for a unit as well as the time by which she must make the purchase are private information. In this environment,
we derive the revenue maximizing Bayesian incentive compatible selling mechanism.

Characterization of Revenue Equivalence, 2007, with B.Heydenreich, Rudolf Muller and Marc Uetz.

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called \emph{revenue equivalence}. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints.

The characterization holds for any (possibly infinite) outcome space and many of the known results about revenue equivalence are immediate consequences

Paths, Cycles and Mechanism Design , 2007. (Updated 2008)

The incentive compatibility constraints of mechanism design (with quasi-linear utilities) can be interpreted as being the dual inequalities of a shortest path problem. I believe this interpretation provides an intuitive and powerful lens through which to view the implications of incentive compatibility.

This document provides an (incomplete) account of the main results in mechanism design from this point of view. They assume familiarity with mechanism design and basic linear programming and convex analysis. I welcome suggestions for additions, deletions and improvements to this material.

Axiomatic characterization of the absolute median on cube-free median networks ,
2006, with H. M. Mulder.

In Vohra (1996) a characterization of the absolute median of a tree network using three simple axioms is presented. This note extends that result from tree networks to cube-free median networks. A special case of such networks is the grid structure of roads found in cities equipped with the Manhattan metric.

Bounds on the Inefficiency of Sequential Auctions, 2006, with Junjik Bae, Eyal Beigman, Randall Berry and Micahel Honig.

We study the sequential second price auction of multiple units of a homogeneous commodity. It is well known that such auctions can have inefficient equilibria. For the case of two bidders, we show that the value of the allocation obtained in a the unique subgame perfect equilibrium is at least $1-e^{-1}$ of the value of the efficient allocation. Furthermore, we show that this bound is asymptotically tight.

On Stability of the Core, 2006, with Kamal Jain.

This paper introduces a strengthening of the notion of a stable core and characterizes it in terms of Kikiuta and Shapley's extendability condition.

Non Parametric Learnability of Income-Lipschitz Demand Functions, 2006, with Eyal Beigman.

A sequence of prices and demands are rationalizable if there exists a concave, continuous and monotone utility function such that the demands are the maximizers of the utility function over the budget set corresponding to the price. Afriat(1967) presented necessary and sufficient conditions for a finite sequence to be rationalizable. Varian(1982) and later Blundell et al. (2003, 2005) continued this line of work studying nonparametric methods to forecasts demand. Their methods do not implement any probabilistic model and therefore fall short of giving a general degree of confidence in the forecast. The present paper complements this line of research by introducing a statistical model and a measure of complexity through which we are able to study the learnability of classes of demand functions and derive a degree of confidence in the forecasts.

In this paper we develop a framework to study the learnability of real vector valued demand functions through observations on prices and demand. Our results give lower and upper bounds on the sample complexity of PAC learnability and show that the sample complexity of learning a class of vector valued functions with finite fat shattering dimension increases by a linear factor of the dimension. We show that classes of income-Lipschitz demand functions with global bounds on the Lipschitz constant have finite fat shattering dimension.

Optimal Auctions for Asymmetrically Budget Constrained Bidders, 2005, with Alexey Malakhov.

We consider an environment with a single divisible good and two bidders. The valuations of the bidders are private information but one bidder has a commonly known budget constraint. For this environment we derive the revenue maximizing subsidy free incentive compatible auction. We also examine the case when the budget constraint is private information but bidders must post a bond.

Single and Multi-Dimensional Optimal Auctions: A Network Approach, 2004, with Alexey Malakhov.

This paper highlights connections between the discrete and continuous approaches to optimal auction design with single and multi-dimensional types. We provide an interpretaion of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice. We also solve some cases explicitly in the discrete framework.