## Working Papers

**Private Private Information** (with Fedor Sandomirskiy and Omer Tamuz)

[abstract] [download pdf] [arXiv]

*private*private information structure, agents’ signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information.

**Observability, Dominance, and Induction in Learning Models** (with Daniel Clark and Drew Fudenberg)

[abstract] [download pdf] [arXiv]

*terminal node partitions*so that two games are

*information equivalent*, i.e., the players receive the same feedback about others’ strategies.

**Screening p-Hackers: Dissemination Noise as Bait** (with Federico Echenique)

[abstract] [download pdf] [arXiv]

*p*-hacked findings: spurious explanations of the outcome variable produced by attempting multiple econometric specifications. Noise creates “baits” that attract

*p*-hackers, who engage in data mining with no prior information about the true cause behind the outcome, inducing them to report verifiably wrong results. But, noise only minimally impacts honest researchers who use data to test an ex-ante hypothesis about the causal mechanism. We characterize the optimal level of dissemination noise and highlight the relevant tradeoffs in a simple theoretical model. Dissemination noise is a tool that statistical agencies (e.g., the US Census Bureau) currently use to protect privacy, and we show this existing practice can be repurposed to improve research credibility.

**Evolutionarily Stable (Mis)specifications: Theory and Applications** (with Jonathan Libgober)

Presented at *ACM EC’21*.

[abstract] [download pdf] [arXiv]

*evolutionarily stable*against another if, whenever sufficiently prevalent, its adherents obtain higher average payoffs than their counterparts. Agents’ equilibrium beliefs are constrained but not wholly determined by specifications. Endogenous belief formation through the learning channel generates novel stability phenomena compared to frameworks where single beliefs are the heritable units of cultural transmission. In linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure, the correct specification is evolutionarily unstable against a correlational error whose direction depends on social interaction structure. We also endogenize coarse thinking in games and show how its prevalence varies with game parameters.

**Aggregative Efficiency of Bayesian Learning in Networks** (with Krishna Dasaratha)

Revision requested at *Econometrica*.

Best Paper Award and Best Student Paper Award at *ACM EC’21*.

[abstract] [download pdf] [slides] [EC'21 talk] [arXiv]

*aggregative efficiency*index. Networks where agents observe multiple neighbors but not their common predecessors

*confound*information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

**Dynamic Information Design with Diminishing Sensitivity Over News** (with Jetlir Duraj)

[abstract] [download pdf] [online appendix] [slides] [arXiv]

## Published Papers

**Mislearning from Censored Data: The Gambler’s Fallacy and Other Correlational Mistakes in Optimal-Stopping
Problems**

Forthcoming at *Theoretical Economics*.

[abstract] [download pdf] [arXiv]

**Network Structure and Social Learning** (with Krishna Dasaratha)

*ACM SIGecom Exchanges* 19(2):62–67, November 2021.

[abstract] [download pdf] [publisher’s DOI]

**An Experiment on Network Density and Sequential Learning** (with Krishna Dasaratha)

*Games and Economic Behavior* 128:182-192, July 2021. Presented at *ACM EC’20*.

[abstract] [download pdf] [slides] [publisher’s DOI] [pre-registration] [data and code] [EC’20 talk] [arXiv]

**Player-Compatible Learning and Player-Compatible Equilibrium** (with Drew Fudenberg)

*Journal of Economic Theory* 194:105238, June 2021.

[abstract] [download
pdf] [online
appendix] [publisher’s DOI] [arXiv]

*Player-Compatible Equilibrium*(PCE) imposes cross-player restrictions on the magnitudes of the players’ “trembles” onto different strategies. These restrictions capture the idea that trembles correspond to deliberate experiments by agents who are unsure of the prevailing distribution of play. PCE selects intuitive equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We show that rational learning and weighted fictitious play imply our compatibility restrictions in a steady-state setting.

**Network Structure and Naive Sequential Learning** (with Krishna Dasaratha)

*Theoretical Economics* 15(2):415–444, May 2020.

[abstract] [download pdf]
[publisher’s DOI] [arXiv]

**Payoff Information and Learning in Signaling Games** (with Drew Fudenberg)

*Games and Economic Behavior* 120:96-120, March 2020.

[abstract] [download
pdf] [publisher’s DOI] [arXiv]

*rationality-compatible equilibria*(

*RCE*), and bounded below by

*uniform RCE*. RCE refine the Intuitive Criterion (Cho and Kreps, 1987) and include all divine equilibria (Banks and Sobel, 1987). Uniform RCE sometimes but not always exists, and implies universally divine equilibrium.

**Learning and Type Compatibility in Signaling Games** (with Drew Fudenberg)

*Econometrica* 86(4):1215-1255, July 2018.

[abstract] [download
pdf] [online appendix] [publisher’s DOI] [arXiv]

**Bayesian Posteriors for Arbitrarily Rare Events** (with Drew Fudenberg and Lorens Imhof)

*Proceedings of the National Academy of Sciences* 114(19):4925-4929, May 2017.

[abstract] [download pdf] [publisher’s DOI] [arXiv]

**Differentially Private and Incentive Compatible Recommendation System for the
Adoption of Network Goods** (with Xiaosheng
Mu)

*Proceedings of the 15th ACM Conference on Economics and Computation
(ACM EC’14)*:949-966, June 2014.

[abstract] [download pdf] [slides]
[publisher’s DOI]

## Current Classes

I'm teaching!

Classes will meet online until the university resumes in-person teaching. See Canvas for details. If you are enrolled but have trouble accessing Canvas, let me know.

**Game Theory and Applications** (ECON 682)

An introduction to game theory aimed at graduate students in SAS/SEAS/Wharton.

[syllabus] [canvas]

**Topics in Advanced Economic Theory and Mathematical Economics** (ECON 712)

A topics class for Ph.D. students in Economics, featuring a few of my favorite things: learning in games, learning in networks, and learning with psychological agents.

[syllabus] [canvas]