Working Papers
Learning from Viral Content (with Krishna Dasaratha)
Revise and resubmit at the American Economic Review.
Presented at ACM EC’24.
[abstract] [download pdf] [arXiv]
We study learning on social media with an equilibrium model of users interacting with shared news stories. Rational users arrive sequentially, observe an original story (i.e., a private signal) and a sample of predecessors’ stories in a news feed, and then decide which stories to share. The observed sample of stories depends on what predecessors share as well as the sampling algorithm generating news feeds. We focus on how often this algorithm selects more viral (i.e., widely shared) stories. Showing users viral stories can increase information aggregation, but it can also generate steady states where most shared stories are wrong. These misleading steady states self-perpetuate, as users who observe wrong stories develop wrong beliefs, and thus rationally continue to share them. Finally, we describe several consequences for platform design and robustness.
Private Private Information (with Fedor Sandomirskiy and Omer Tamuz)
Revise and resubmit at the Journal of Political Economy.
Presented at ACM EC’22.
[abstract] [download pdf] [slides] [talk] [arXiv]
Private signals model noisy information about an unknown state. Although these signals are called “private,” they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.
Aggregative Efficiency of Bayesian Learning in Networks (with Krishna Dasaratha)
Revise and resubmit at Econometrica.
Best Paper Award at ACM EC’21.
[abstract] [download pdf] [slides] [EC'21 talk] [arXiv]
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 log-linear functions of observations and admit a signal-counting interpretation of accuracy. Networks where agents observe multiple neighbors but not their common predecessors confound information, and even a small amount of confounding can lead to much lower accuracy. In a class of networks where agents move in generations and observe the previous generation, we quantify the information loss with an aggregative efficiency index. Aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Later generations contribute little additional information, even with arbitrarily large generations.
Misspecified Learning and Evolutionary Stability (with Jonathan Libgober)
[abstract] [download pdf]
Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their environment through repeated play. The relative stability of (mis)specifications depends on their adherents’ equilibrium payoffs. A key mechanism is the learning channel: the endogeneity of perceived best replies due to inference. We characterize when a rational society is only vulnerable to invasion by some misspecification through the learning channel, and highlight new stability phenomena that arise due to the learning channel. As an application, we show how our framework can be used to endogenize coarse analogy classes in centipede games.
Higher-Order Beliefs and (Mis)learning from Prices (with Jonathan Libgober)
Revise and resubmit at the American Economic Journal: Microeconomics.
[abstract] [download pdf]
We study misperceptions of private-signal correlation in a setting where a population repeatedly matches up to play an incomplete-information Cournot duopoly game. We show that a misperception’s viability can depend on whether agents hold flexible or dogmatic beliefs about price elasticity. If agents have flexible beliefs and learn elasticity by observing prices, correlation misperceptions indirectly distort behavior through elasticity misinference. If agents dogmatically know elasticity with certainty, this learning channel is eliminated. The direct and indirect effects of correlation misperception on behavior oppose each other, implying that the possibility of elasticity inference can reverse an error’s viability.
Published Papers
Dynamic Information Preference and Communication with Diminishing Sensitivity Over News (with Jetlir Duraj)
Theoretical Economics 19(3):1057–1086, July 2024.
[abstract] [download pdf] [publisher’s DOI] [slides] [arXiv]
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. Diminishing sensitivity induces a preference over news skewness: gradual bad news, one-shot good news is worse than one-shot resolution, which is in turn worse than gradual good news, one-shot bad news. So, the agent's preference between gradual information and one-shot resolution can depend on his consumption ranking of different states. In a dynamic cheap-talk framework where a benevolent sender communicates the state over multiple periods, the babbling equilibrium is essentially unique when the receiver is not loss averse. Contrary to the commitment case, more loss-averse receivers may enjoy higher news utility in equilibrium. We characterize the family of gradual good news equilibria when facing such receivers and find the sender conveys progressively larger pieces of good news.
Screening p-Hackers: Dissemination Noise as Bait (with Federico Echenique)
Proceedings of the National Academy of Sciences 121(21):e2400787121, May 2024. Presented at ACM EC’22.
[abstract] [download pdf] [publisher’s DOI] [arXiv]
We show that adding noise before publishing data effectively screens p-hacked findings: spurious explanations produced by fitting many statistical models (data mining). Noise creates “baits” that affect two types of researchers differently. Uninformed p-hackers, who are fully ignorant of the true mechanism and engage in data mining, often fall for baits. Informed researchers, who start with an ex-ante hypothesis, are minimally affected. We show that as the number of observations grows large, dissemination noise asymptotically achieves optimal screening. In a tractable special case where the informed researchers’ theory can identify the true causal mechanism with very little data, we characterize the optimal level of dissemination noise and highlight the relevant trade-offs. Dissemination noise is a tool that statistical agencies currently use to protect privacy. We argue this existing practice can be repurposed to screen p-hackers and thus improve research credibility.
Observability, Dominance, and Induction in Learning Models (with Daniel Clark and Drew Fudenberg)
Journal of Economic Theory 206:105569, December 2022.
[abstract] [download pdf] [publisher’s DOI] [arXiv]
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.
Mislearning from Censored Data: The Gambler’s Fallacy and Other Correlational Mistakes in Optimal-Stopping
Problems
Theoretical Economics 17(3):1269–1312, July 2022.
[abstract] [download pdf] [publisher’s DOI] [arXiv]
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.
[abstract] [download pdf] [publisher’s DOI]
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.
[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]
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.
[abstract] [download
pdf] [publisher’s DOI] [arXiv]
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.
[abstract] [download
pdf] [online appendix] [publisher’s DOI] [arXiv]
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.
[abstract] [download pdf] [publisher’s DOI] [arXiv]
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.
[abstract] [download pdf] [slides]
[publisher’s DOI]
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.
Deprecated Paper
Evolutionarily Stable (Mis)specifications: Theory and Applications (with Jonathan Libgober)
Subsumed by “Misspecified Learning and Evolutionary Stability” and “Higher-Order Beliefs and (Mis)learning from Prices.”
Presented at ACM EC’21.
[abstract] [download pdf] [arXiv]
Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their environment through repeated play. The relative stability of (mis)specifications depends on their adherents’ equilibrium payoffs. A key mechanism is the learning channel: the endogeneity of perceived best replies due to inference. We characterize when a rational society is only vulnerable to invasion by some misspecification through the learning channel. The learning channel leads to new stability phenomena, and can confer an evolutionary advantage to otherwise detrimental biases in economically relevant applications.
