Quantal response equilibrium as a structural model for estimation: The missing manual

One of the original objectives of the (logit) quantal response equilibrium (LQRE) model was to provide a method for structural estimation of behavior in games, when behavior deviated from Nash equilibrium predictions. To date, only Chapter 6 of the book on quantal response equilibrium by Goeree et al. (2016) focuses on how such estimation can be implemented. We build on that chapter to provide here a more detailed treatment of the methodological issues of implementing maximum likelihood estimation of QRE. We compare the equilibrium correspondence and empirical payoff approaches to estimation, and identify some considerations in interpreting the results of those approaches when applied to the same data on the same game. We also provide a more detailed “field guide” to using numerical continuation methods to accomplish estimation, including guidance on how to tailor implementations to games with different structures.