2022 Theses Doctoral

# Essays on Econometric Analysis of Game-theoretic Models

This dissertation studies econometric analysis of game-theoretic models. I develop novel empirical models and methodologies to facilitate robust and computationally tractable econometric analysis.

In Chapter 1, I develop an empirical model for analyzing stable outcomes in the presence of incomplete information. Empirically, many strategic settings are characterized by stable outcomes in which players’ decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations, I build an empirical framework by introducing a novel solution concept that I call Bayes stable equilibrium. The framework allows the researcher to be agnostic about players’ information and the equilibrium selection rule. Furthermore, I show that the Bayes stable equilibrium identiﬁed set is always weakly tighter than the Bayes correlated equilibrium identiﬁed set; numerical examples show that the shrinkage can be substantial. I propose computationally tractable approaches for estimation and inference and apply the framework to study the strategic entry decisions of McDonald’s and Burger King in the US.

In Chapter 2, I study identiﬁcation and estimation of a class of dynamic games when the underlying information structure is unknown to the researcher. I introduce Markov correlated equilibrium, a dynamic analog of Bayes correlated equilibrium studied in Bergemann and Morris (2016), and show that the set of Markov correlated equilibrium predictions coincides with the set of Markov perfect equilibrium predictions that can arise when the players might observe more signals than assumed by the analyst. I propose an econometric approach for estimating dynamic games with weak assumption on players’ information using Markov correlated equilibrium. I also propose multiple computational strategies to deal with the non-convexities that arise in dynamic environments.

In Chapter 3, I propose an extremely fast and simple approach to estimating static discrete games of complete information under pure strategy Nash equilibrium and no assumptions on the equilibrium selection rule. I characterize an identiﬁed set of parameters using a set of inequalities that are expressed in terms of closed-form multinomial logit probabilities. The key simpliﬁcations arise from using a subset of all identifying restrictions that are particularly easy to handle. Under standard assumptions, the identiﬁed set is convex and its projections can be obtained via convex programs. Numerical examples show that the identiﬁed set is quite tight. I also propose a simple approach to construct conﬁdence sets whose projections can be obtained via convex programs. I demonstrate the usefulness of the approach using real-world data.

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## Subjects

## Files

- Koh_columbia_0054D_17130.pdf application/pdf 3.63 MB Download File

## More About This Work

- Academic Units
- Economics
- Thesis Advisors
- Lee, Sokbae
- Salanie, Bernard
- Degree
- Ph.D., Columbia University
- Published Here
- April 13, 2022