About Jeffrey Ely

Jeff Ely is the Charles E. and Emma H. Morrison Professor of Economics at Northwestern University and an accomplished latte-artist. He is the director of the Program in Mathematical Methods in the Social Sciences at Northwestern, a member of several editorial boards and co-author of the blog Cheap Talk.

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.

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.

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.

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.

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.