## ALFRED GALICHON'S

## MASTERCLASSES

November 24, 5pm Paris time / 11am NY time

Timothy Christensen

(New York University)

Counterfactual Sensitivity and Robustness (joint with Benjamin Connault)

Abstract: We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite-dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite-dimensional convex program. We develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug-in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to welfare analysis in matching models with transferable utility and dynamic discrete choice models.

December 8 2022, 5pm Paris time / 11am NY time

Marcin Pęski

(University of Toronto)

Fuzzy Conventions

Abstract: We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy - it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically depends on the network. The largest set (in the set inclusion sense) is achieved by a network that consists of a large number of copies of a large complete graph. The smallest set (in the set inclusion sense) is achieved in a lattice-type network. It consists of a single outcome that corresponds to a novel version of risk dominance that is appropriate for games with random utility.

February 9 2023, 5pm Paris time / 11am NY time

Junjie Zhou

(Tsinghua University)

Network games made simple (joint with Yves Zenou)

Abstract: Most network games assume that the best response of a player is a linear function of the actions of her neighbors; clearly, this is a restrictive assumption. We developed a theory called sign-equivalent transformation (SET) underlying the mathematical structure behind a system of equations defining the Nash equilibrium. By applying our theory, we reveal that many network models in the existing literature, including those with nonlinear best responses, can be transformed into games with best-response potentials after appropriate restructuring of equilibrium conditions using SET. Thus, through our theory, we produce a unified framework that provides conditions for existence and uniqueness of equilibrium for most network games with both linear and nonlinear best-response functions. We also provide novel economic insights for both the existing network models and the new ones we develop in this study.