Research

Working papers

1. "Optimal screening contests"

   
   PDF Abstract

   We study the optimal design of contests as screening devices. In an incomplete information environment, contest results reveal information about the quality of the participating agents at the cost of potentially wasteful effort put in by these agents. We are interested in finding contests that maximize the information revealed per unit of expected effort put in by the agents. In a model with linear costs of effort and privately known marginal costs, we find the Bayes-Nash equilibrium strategy for arbitrary prize structures (\(1=v_1 \geq v_2 \dots \geq v_n=0\)) and show that the equilibrium strategy mapping marginal costs to effort is always a density function. It follows then that the expected effort under the uniform prior on marginal costs is independent of the prize structure. Restricting attention to a simple class of uniform prizes contests (top \(k\) agents get \(1\) and others get \(0\)), we find that the optimal screening contest under the uniform prior awards half as many prizes as there are agents. For the power distribution \(F(\theta)=\theta^p\) with \(p\geq 1\), we conjecture that the number of prizes in the optimal screening contest is decreasing in \(p\). In addition, we also show that a uniform prize structure is generally optimal for the standard objectives of maximizing expected effort of an arbitrary agent, most efficient agent and least efficient agent.

2. "Stable allocations in discrete economies"

   (with Federico Echenique and SangMok Lee)
   PDF Abstract

   We study discrete allocation problems, as in the textbook notion of an exchange economy, but with indivisible goods. The problem is well-known to be difficult. The model is rich enough to encode some of the most pathological bargaining configurations in game theory, like the roommate problem. Our contribution is to show the existence of stable allocations (outcomes in the weak core, or in the bargaining set) under different sets of assumptions. Specifically, we consider dichotomous preferences, categorical economies, and discrete TU markets. The paper uses varied techniques, from Scarf's balanced games to a generalization of the TTC algorithm by means of Tarski fixed points.

3. "Project selection with partially verifiable information"

   (with Wade Hann-Caruthers)
   PDF Abstract

   We consider a principal agent project selection problem with asymmetric information. There are N projects and the principal must select exactly one of them. Each project provides some profit to the principal and some payoff to the agent and these profits and payoffs are the agent's private information. We consider the principal's problem of finding an optimal mechanism for two different objectives: maximizing expected profit and maximizing the probability of choosing the most profitable project. Importantly, we assume partial verifiability so that the agent cannot report a project to be more profitable to the principal than it actually is. Under this no-overselling constraint, we characterize the set of implementable mechanisms. Using this characterization, we find that in the case of two projects, the optimal mechanism under both objectives takes the form of a simple cutoff mechanism. The simple structure of the optimal mechanism also allows us to find evidence in support of the well-known ally-principle which says that principal delegates more authority to an agent who shares their preferences.

4. "Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions"

   (with Wade Hann-Caruthers)
   PDF Abstract

   We consider the facility location problem in two dimensions. In particular, we consider a setting where agents have Euclidean preferences, defined by their ideal points, for a facility to be located in \(\mathbb{R}^2\). For the minisum objective and an odd number of agents, we show that the coordinate-wise median mechanism (CM) has a worst-case approximation ratio (AR) of \(\sqrt{2}\frac{\sqrt{n^2+1}}{n+1}\). Further, we show that CM has the lowest AR for this objective in the class of deterministic, anonymous, and strategyproof mechanisms. For the p-norm social welfare objective, we find that the AR for CM is bounded above by \(2^{\frac{3}{2}-\frac{2}{p}}\) for \(p\geq 2\). Since any deterministic strategyproof mechanism must have AR at least \(2^{1-\frac{1}{p}}\) (Feigenbaum et al. (2017)), our upper bound suggests that the CM is (at worst) very nearly optimal. We conjecture that the approximation ratio of coordinate-wise median is actually equal to the lower bound \(2^{1-\frac{1}{p}}\) (as is the case for \(p=2\) and \(p=\infty\)) for any \(p\geq 2\).

Teaching

Instructor at Econschool

Econschool is an initiative to assist undergraduate students in India who wish to pursue higher studies in Economics. As an instructor, I've taught a course on mathematics for economists and also helped with the development and delivery of various online resources.

Teaching Assistant at Caltech

• Ec 122: Econometrics (Fall 2018-19, Fall 2019-20)
• Ec 11: Introduction to Economics (Winter 2018-19)
• BEM 103: Introduction to finance (Winter 2019-20, Winter 2021-22)
• PS/Ec 172: Game theory (Spring 2019-20)
• Ec 121A: Theory of Value (Fall 2021-22)
• CS/Ec 149: Algorithmic Economics (Spring 2021-22)

Contact information

Address

Sumit Goel
Division of the Humanities and Social Sciences
Mail Code 228-77
California Institute of Technology
Pasadena, CA 91125

Office

218 Baxter Hall

Email

sgoel [at] caltech [dot] edu