Job Market Paper
Modeling Statistically Robust Learners in HighDimensional Environments
Economic models generally assume agents learn according to the classical Bayesian paradigm, or else view departures from that paradigm as the result of behavioral biases or cognitive limitations. Yet when researchers in economics and statistics are themselves learning how to model something  in particular, when they are trying to learn potentially highdimensional models  their approach is increasingly guided by not by a Bayesian prior but the objective of statistically robust performance: guarantees that their learning rule will select an approximately bestperforming model in some class no matter the true datagenerating process. This paper develops a framework for modeling statistically robust learners. First, we formalize a general notion of statistical robustness that applies to learning from potentially indirect and heterogeneous sources of information, and then extend the classical Vapnik–Chervonenkis learnability results to this setting to give a sharp characterization of when robust learning is possible. Second, we show that robust learning is fundamentally different from Bayesian learning in complex learning problems with misspecification by proving an upper bound on the robustness guarantees of Bayesian learning for any prior. Third, we apply these results to define statistically robust learning equilibrium in games, which replaces the bestfit condition of BerkNash equilibrium with optimal robust learning conditions. An application to an asset trading game illustrates that statistically robust equilibrium can provide more intuitively appealing predictions than modeling agents as misspecified Bayesian learners.
Papers
On the Probability of the Existence of Pairwise Stable Networks
Since its introduction in Jackson and Wolinsky, 1996, pairwise stability has been the
preponderant equilibrium notion for network formation games in both the theoretical
and applied networks literatures. Yet pairwise stable networks do not exist in some
network formation settings, and the known conditions which ensure existence with
deterministic preferences are too restrictive to cover all but a highlyspecialized set of
cases. In this paper, we analyze the probability of the existence of pairwise stable
networks in network formation settings with random utilities. Our results show that, in
a broad range of settings that includes many standard empirical specifications, pairwise
stable networks exist with high probability in network formation settings with many
agents.
Behavioral Communities and Atomic Structure of Networks (w/ Matt Jackson)
We develop a method of detecting the ‘behavioral communities’ of a social network
based on how people act when they choose their behaviors in coordination with their
friends’ behaviors. There can be multiple different ‘conventions’ (equilibria) in which
people in some parts of the network adopt a behavior while people in other parts of the
network do not. We define atoms/communities to be groups of people who behave the
same as each other in every convention. This provides a microfoundation for a method
of detecting communities in social and economic networks. We characterize such behavioral communities in some random graphs as a function of how strongly the benefits
of adopting the behavior depend on others’ behaviors. We also discuss applications including: optimally seeding the di↵usion of behaviors involving peer influence, detecting
which demographics or nodal characteristics define a society’s communities, estimating
the strength of peer influence on behavior, as well as identifying missing network data by
observing a series of conventions.
Work in Progress
Myopic Equilibria in Network Formation via Expander Graphs
We study when myopic behavior constitutes an approximate equilibrium in a decentralized, cumulative offer trading network formation game. We show that when firms’ preferences satisfy full substitutability, the formation game implements a stable outcome of the related cooperative game, and so an epsilonBayes Nash Equilibrium in myopic strategies exists if and only if there is a stable mechanism which is epsilonBayesian incentive compatible. A sufficient condition for the existence of an epsilonBayesian incentive compatible stable mechanism is that influence graphs, which track how manipulations propagate through the network, belong to the class of vertexexpander graphs.
