# Kevin He

Assistant Professor
University of Pennsylvania

[curriculum vitae]

## Working Papers

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

We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over a correct specification. Agents with heterogeneous specifications coexist in a society and repeatedly match against random opponents to play a stage game. They draw Bayesian inferences about the environment based on personal experience, so their learning depends on the distribution of specifications and matching assortativity in the society. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher expected objective payoffs than their counterparts. The learning channel leads to novel stability phenomena compared to frameworks where the heritable unit of cultural transmission is a single belief instead of a specification (i.e., set of feasible beliefs). We apply the framework to linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure. The correct specification is not evolutionarily stable against a correlational error, whose direction depends on matching assortativity. As another application, the framework also endogenizes coarse analogy classes in centipede games.

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

In social-learning settings where individuals receive private signals and observe network neighbors’ actions, the network structure often obstructs information aggregation. We consider sequential social learning with rational agents and Gaussian signals and ask how the efficiency of signal aggregation changes with the network. Rational actions in our model admit a signal-counting interpretation of accuracy, which lets us compare the aggregative efficiency of social learning across networks. Learning is very inefficient in a class of networks where agents move in generations and observe the previous generation. Generations after the first contribute very little additional information, 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.

Mislearning from Censored Data: The Gambler’s Fallacy in Optimal-Stopping Problems
Revision requested at Theoretical Economics.

I study endogenous learning dynamics for people expecting systematic reversals from random sequences — the “gambler's fallacy.” 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’ experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution’s mean and stops too early. Agents uncertain about the distribution’s variance overestimate it to an extent that depends on predecessors’ stopping thresholds. Subsidizing search partially mitigates long-run belief distortions.

## Published Papers

An Experiment on Network Density and Sequential Learning (with Krishna Dasaratha)
Games and Economic Behavior 128:182-192, July 2021. Presented at 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 (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

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]

## Past Classes

Intermediate Microeconomics - Advanced (ECON 1011A, as TA)
This course teaches the basic tools of economics and their applications to a wide range of human behavior.
[syllabus]   [section notes]   [teaching evaluations]

Economic Theory (ECON 2010A, as TA)
Topics include extensive- and normal-form games, Nash equilibrium, rationalizability, Nash implementation, auctions, bargaining, repeated games, signaling, and forward induction.
[syllabus]   [section notes]   [teaching evaluations]