Optimal Feedback in Contests

We derive optimal contests for environments where output takes the form of breakthroughs and the principal has an informational advantage over the contestants. Whether or not the principal is able to provide real-time feedback to contestants, the optimal prize allocation is egalitarian: all agents who have succeeded in a pre-specified time interval share the prize equally. When providing feedback is feasible, the optimal contest takes a stark cyclical form: contestants are fully apprised of their own success, and at the end of each fixed-length cycle, they are informed about peer success as well.

Joint with George Georgiads, Sina Khorasani and Luis Rayo

Rotation as Contagion Mitigation

We study rotation schemes that govern individuals’ activities within an organization during an epidemic. We optimize the frequency of rotation and degree of cross-mixing of the rotating subpopulations. Frequency affects risk over the length of diffusion within the infected subpopulation until the organization detects and/or reacts to the infection. If the reaction time is short, then such risk is undesirable since the growth of the prevalence is initially convex in time. Frequent rotation, which acts as insurance against exposure time risk, is then optimal. Infrequent rotation becomes optimal if the organization reacts slowly. Mixing of the rotating subpopulations is detrimental because it increases the share of interactions between sick and healthy individuals. However, the effect of mixing is small if the terminal prevalence is low in the absence of mixing.

Joint with Andrea Galeotti and Jakub Steiner

Optimal Test Allocation

A health authority chooses a binary action for each of several individuals that differ in their pre-test probabilities of being infected and in the additive losses associated with two types of decision errors. The authority is endowed with a portfolio of tests that differ in their sensitivities and specificities. We derive a simple necessary condition for optimality of test allocation. In special cases, precision parameters of the allocated test are monotone in the individuals’ types. We characterize the marginal benefit of a test and provide an algorithmic solution for the test-allocation problem.

Joint with Jakub Steiner and Andrea Galeotti

Sequential Information Design

We study games of incomplete information as both the information structure and the extensive-form vary. An analyst may know the payoff-relevant data but not the players' private information, nor the extenstive-form that governs their play. Alternatively, a designer may be able to build a mechanism from these ingredients. We characterize all outcomes that can arise in an equilibrium of some extensive-form with some information structure. We do this for a range of extensive-form solution concepts.

Joint with Laura Doval

A Cake-Cutting Solution to Gerrymandering

I propose a mechanism for redistricting inspired by cake-cutting mechanisms for fair division. The majority party proposes a partition of a state into districts. The minority party can accept it or undo any partisan disadvantage caused by irregular boundaries. Thus without imposing any requirement of regularity, the mechanism ensures that to the extent that irregular districts result from the process, the minority is never harmed by them.

Moving the Goalposts

Joint with Martin Szydlowski

We study information as an incentive device in a dynamic moral hazard frame- work. An agent works on a task of uncertain difficulty, modeled as the duration of required effort. The principal knows the task difficulty and can provide informa- tion over time with the goal of inducing maximal effort. The optimal mechanism features moving goalposts: an initial disclosure makes the agent sufficiently opti- mistic that the task is easy in order to induce him to start working. If the task is indeed difficult the agent is told this only after working long enough to put the dif- ficult task within reach. Then the agent completes the difficult task even though he never would have chosen to at the outset. The value of dynamic disclosure implies that principal prefers a random threshold over any deterministic scheme. We con- sider extensions to two-player pre-emption games and bandits.

Beeps

I introduce and study dynamic persuasion mechanisms. A principal privately observes the evolution of a stochastic process and sends messages over time to an agent. The agent takes actions in each period based on her beliefs about the state of the process and the principal wishes to influence the agent’s action. I characterize the optimal persuasion mechanism and show how to derive it in applications. I then consider the extension to multiple agents where higher-order beliefs matter.

My Google Scholar Page

Teaching

Intermediate Micro Course

I teach undergraduate intermediate microeconomics, a 10 week course that is the second in a two-part seqeunce at Northwestern University. I have developed a unique approach to intermediate micro based originally on a course designed by my former colleague Kim-Sau Chung. The goal is to study the main themes of microeconomics from an institution- and in particular market-free approach. To illustrate what I mean, when I cover public goods, I do not start by showing the inefficiency of market provided public goods. Instead I ask what are the possibilities and limitations of any institution for providing public goods. By doing this I illustrate the basic difficulty without confounding it with the additional problems that come from market provision. I do similar things with externalities, informational asymmetries, and monopoly.

All of this is done using the tools of dominant-strategy mechanism design. This enables me to talk about basic economic problems in their purest form. Once we see the problems posed by the environments mentioned above, we investigate efficiency in the problem of allocating private goods with no externalities. A cornerstone of the course is a dominant-strategy version of the Myerson-Satterthwaite theorem which shows the basic friction that any institution must overcome. We then investigate mechanisms for efficient allocation in large economies and we see that the institutions that achieve this begin to resemble markets.

Only at this stage do markets become the primary lens through which to study microeconomics. We look at a simple model competition among profit-maximizing auctioneers and a sketch of convergence to competitive equilibrium. Then we finish with a brief look at general equilibrium in pure exchange economies and the welfare theorems.

There is a minimal amount of game theory, mostly just developing the tools necessary to use mechanism design in dominant strategies, but also a side trip into Nash equilibrium and mixed strategies.

Course Content