# Kevin He

Assistant Professor
University of Pennsylvania

[curriculum vitae]

## Working Papers

Private Private Information (with Fedor Sandomirskiy and Omer Tamuz)
Presented at ACM EC’22.

In a 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 cannot be made more informative 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)
Revised and resubmitted to the Journal of Economic Theory.

Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of “forward induction,” because rational agents may use dominated strategies as experiments to learn how opponents play, and may not have enough data to rule out a strategy that opponents never use. Learning models also do not support the idea that the selected equilibria should only depend on a game’s reduced normal form. However, playing the extensive form of a game is equivalent to playing the normal form augmented with the appropriate 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)
Presented at ACM EC’22.

We show that adding noise to data before making data public is effective at screening p-hacked findings: spurious explanations of the outcome variable produced by attempting multiple econometric specifications. Noise creates “baits” that affect two types of researchers differently. Uninformed p-hackers, who engage in data mining with no prior information about the true causal mechanism, often fall for baits and report verifiably wrong results when evaluated with the original data. But informed researchers, who start with an ex-ante hypothesis about the causal mechanism before seeing any data, are minimally affected by noise. We characterize the optimal level of dissemination noise and highlight the relevant trade-offs 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.

We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations and help explain the persistence of behavioral biases. Agents with heterogeneous specifications coexist in a society and repeatedly play a stage game against random opponents. Based on personal experience, agents draw Bayesian inferences about the uncertain environment. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher average payoffs than their counterparts. Since equilibrium beliefs are constrained but not wholly determined by specifications, the underlying environment influences perceived best replies. This property expands the scope for misspecifications to invade a rational society: the correct specification may fail to be evolutionarily stable only when invaders infer from data. We also identify new stability phenomena which are generated by this endogeneity of perceived best replies. Applications of our framework include projection bias, correlation neglect, and analogy-based reasoning. As an illustration, in an incomplete-information Cournot duopoly game where players possibly misperceive the information structure, a biased perception may be beneficial when players infer the market price elasticity, yet harmful when dogmatic over it.

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.

When individuals in a social network learn about an unknown state from private signals and neighbors’ actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their 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)

A Bayesian agent experiences gain-loss utility each period over changes in belief about future consumption (“news utility”), with diminishing sensitivity over the magnitude of news. We show the agent’s preference between an information structure that delivers news gradually and another that resolves all uncertainty at once depends on his consumption ranking of different states. One-shot resolution is better than gradual bad news, but it is not optimal among all information structures (under common functional forms). In a dynamic cheap-talk framework where a benevolent sender communicates the state over multiple periods, the babbling equilibrium is essentially unique without loss aversion. More loss-averse agents may enjoy higher news utility in equilibrium, contrary to the commitment case. We characterize the family of gradual good news equilibria that exist with high enough loss aversion, and find the sender conveys progressively larger pieces of good news. We discuss applications to media competition and game shows.

## Published Papers

Mislearning from Censored Data: The Gambler’s Fallacy and Other Correlational Mistakes in Optimal-Stopping Problems
Theoretical Economics 17(3):1269–1312, July 2022.

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are “good enough,” so predecessors’ experiences contain negative streaks but not positive streaks. When agents wrongly expect systematic reversals (the “gambler's fallacy”), they understate the likelihood of consecutive below-average draws, converge to over-pessimistic beliefs about the distribution’s mean, and stop too early. Agents uncertain about the distribution’s variance overestimate it to an extent that depends on predecessors’ stopping thresholds. I also analyze how other misperceptions of intertemporal correlation interact with endogenous data censoring.

Network Structure and Social Learning (with Krishna Dasaratha)
ACM SIGecom Exchanges 19(2):62–67, November 2021.

We describe results from Dasaratha and He (2021) and Dasaratha and He (2020) about how network structure influences social learning outcomes. These papers share a tractable sequential model that lets us compare learning dynamics across networks. With Bayesian agents, incomplete networks can generate informational confounding that makes learning arbitrarily inefficient. With naive agents, related forces can lead to mislearning.

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]

We conduct a sequential social-learning experiment where subjects each guess a hidden state based on private signals and the guesses of a subset of their predecessors. A network determines the observable predecessors, and we compare subjects’ accuracy on sparse and dense networks. Accuracy gains from social learning are twice as large on sparse networks compared to dense networks. Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the finding is difficult to reconcile with rational-learning models.

Player-Compatible Learning and Player-Compatible Equilibrium (with Drew Fudenberg)
Journal of Economic Theory 194:105238, June 2021.

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.

We study a sequential-learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors’ actions. They weigh these actions according the strengths of their social connections to different predecessors. We show this rule arises endogenously when agents wrongly believe others act solely on private information and thus neglect redundancies among observations. We provide a simple linear formula expressing agents’ actions in terms of network paths and use this formula to characterize the set of networks where naive agents eventually learn correctly. This characterization implies that, on all networks where later agents observe more than one neighbor, there exist disproportionately influential early agents who can cause herding on incorrect actions. Going beyond existing social-learning results, we compute the probability of such mislearning exactly. This allows us to compare likelihoods of incorrect herding, and hence expected welfare losses, across network structures. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups.

Payoff Information and Learning in Signaling Games (with Drew Fudenberg)
Games and Economic Behavior 120:96-120, March 2020.

We add the assumption that players know their opponents’ payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period. Inexperienced agents are uncertain about the prevailing distribution of opponents’ play, but believe that opponents never choose conditionally dominated strategies. Agents engage in active learning and update beliefs based on personal observations. Payoff information can refine or expand learning predictions, since patient young senders’ experimentation incentives depend on which receiver responses they deem plausible. We show that with payoff knowledge, the limiting set of long-run learning outcomes is bounded above by 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.

Which equilibria will arise in signaling games depends on how the receiver interprets deviations from the path of play. We develop a micro-foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non-equilibrium learning by populations of patient and long-lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about the behavior of the population of receivers. Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint on the receiver’s off-path beliefs based on “type compatibility” and hence a learning-based equilibrium selection.

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.

We study how much data a Bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare. Each period, either a blue die or a red die is tossed. The two dice land on side 1 with unknown probabilities $$p_1$$ and $$q_1$$, which can be arbitrarily low. Given a data-generating process where $$p_1 \ge c q_1$$, we are interested in how much data is required to guarantee that with high probability the observer's Bayesian posterior mean for $$p_1$$ exceeds $$(1-\delta)c$$ times that for $$q_1$$. If the prior densities for the two dice are positive on the interior of the parameter space and behave like power functions at the boundary, then for every $$\epsilon >0$$, there exists a finite $$N$$ so that the observer obtains such an inference after $$n$$ periods with probability at least $$1-\epsilon$$ whenever $$n p_1 \ge N$$. The condition on $$n$$ and $$p_1$$ is the best possible. The result can fail if one of the prior densities converges to zero exponentially fast at the boundary.

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.

We study the problem of designing a recommendation system for network goods under the constraint of differential privacy. Agents living on a graph face the introduction of a new good and undergo two stages of adoption. The first stage consists of private, random adoptions. In the second stage, remaining non-adopters decide whether to adopt with the help of a recommendation system $$\mathcal{A}$$. The good has network complimentarity, making it socially desirable for $$\mathcal{A}$$ to reveal the adoption status of neighboring agents. The designer’s problem, however, is to find the socially optimal $$\mathcal{A}$$ that preserves privacy. We derive feasibility conditions for this problem and characterize the optimal solution.

## Current Classes

I'm not currently teaching.

## Past Classes

Game Theory and Applications (ECON 682, to be renamed ECON 6110 in Spring 2023)
An introduction to game theory aimed at graduate students in SAS/SEAS/Wharton.
[syllabus]   [teaching evaluations]

Topics in Advanced Economic Theory and Mathematical Economics (ECON 712, to be renamed ECON 8000 in Spring 2023)
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]   [teaching evaluations]