Identification of dynamic games with unobserved heterogeneity and multiple equilibria

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 intermediate periods to link different decompositions.