Identification of Dynamic Games With Unobserved Heterogeneity and Multiple Equilibria

58 Pages Posted: 9 Aug 2018 Last revised: 20 Oct 2020

See all articles by Yao Luo

Yao Luo

University of Toronto - Department of Economics

Ping Xiao

affiliation not provided to SSRN

Ruli Xiao

Indiana University

Date Written: Oct 19, 2020

Abstract

This paper provides sufficient conditions for nonparametrically identifying dynamic games with incomplete information, allowing for multiple equilibria and payoff-relevant unobservables. Our identification involves two steps. We first identify the equilibrium conditional choice probabilities and state transitions using the Markov property and four-period data. The first step of our identification relies on eigenvalue-eigenvector decomposition, and thus incurs the same issue of identification up-to-label-swapping as the existing literature. This makes it difficult to identify payoff primitives in the second step, which requires consistent matching of unobserved types across different values of the observed variables. Instead of imposing assumptions such as monotonicity, we address this type-matching problem by exploiting the Markov property and longitudinal variations of observables in the middle of the four periods to link different decompositions.

Keywords: Unobserved Heterogeneity, Multiple Equilibria, Discrete Games, Dynamic Games, Nonparametric Identification, Fast Food Chain

JEL Classification: C14, L13

Suggested Citation

Luo, Yao and Xiao, Ping and Xiao, Ruli, Identification of Dynamic Games With Unobserved Heterogeneity and Multiple Equilibria (Oct 19, 2020). Available at SSRN: https://ssrn.com/abstract=3219972 or http://dx.doi.org/10.2139/ssrn.3219972

Yao Luo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

Ping Xiao

affiliation not provided to SSRN

Ruli Xiao (Contact Author)

Indiana University ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

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