  This survey is organized around three main topics: models, econometrics, and
empirical applications. Section 2 presents the theoretical framework,
introduces the concept of Markov Perfect Nash Equilibrium, discusses existence
and multiplicity, and describes the representation of this equilibrium in terms
of conditional choice probabilities. We also discuss extensions of the basic
framework, including models in continuous time, the concepts of oblivious
equilibrium and experience-based equilibrium, and dynamic games where firms
have non-equilibrium beliefs. In section 3, we first provide an overview of the
types of data used in this literature, before turning to a discussion of
identification issues and results, and estimation methods. We review different
methods to deal with multiple equilibria and large state spaces. We also
describe recent developments for estimating games in continuous time and
incorporating serially correlated unobservables, and discuss the use of machine
learning methods to solving and estimating dynamic games. Section 4 discusses
empirical applications of dynamic games in IO. We start describing the first
empirical applications in this literature during the early 2000s. Then, we
review recent applications dealing with innovation, antitrust and mergers,
dynamic pricing, regulation, product repositioning, advertising, uncertainty
and investment, airline network competition, dynamic matching, and natural
resources. We conclude with our view of the progress made in this literature
and the remaining challenges.
