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.
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.
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.
Joint with Alex Frankel and Emir Kamenica
We model demand for non-instrumental information, drawing on the idea that people derive entertainment utility from suspense and surprise. A period has more suspense if the variance of the next period's beliefs is greater. A period has more surprise if
the current belief is further from the last period's belief. Under these denitions, we analyze the optimal way to reveal information over time so as to maximize expected suspense or surprise experienced by a Bayesian audience. We apply our results to the
design of mystery novels, political primaries, casinos, game shows, auctions, and sports.
Joint with Sandeep Baliga
We study torture as a mechanism for extracting information from a suspect who may or may not be informed. We show that a standard rationale for torture generates two commitment problems. First, the principal would benefit from a commitment to torture a suspect he knows to be innocent. Second, the principal would benefit from a commitment to limit the amount of torture faced by the guilty. We analyze a dynamic model of torture in which the credibility of these threats and promises is endogenous. We show that these commit- ment problems dramatically reduce the value of torture and can even render it completely ineffective. We use our model to address ques- tions such as the effect of enhanced interrogation techniques, rights against indefinite detention, and delegation of torture to specialists.
Joint with Marcin Peski
How can we know in advance whether simplifying assumptions about beliefs will make a difference in the conclusions of game-theoretic models? We define critical types to be types whose rationalizable correspondence is sensitive to assumptions about arbitrarily high-order beliefs. We show that a type is critical if and only if it exhibits common belief in some non-trivial event. We use this characterization to show that all types in commonly used type spaces are critical. On the other hand, we show that regular types (types that are not critical) are generic, although perhaps inconvenient to use in applications.
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.