Estimation of Discrete Games with Weak Assumptions on Information

Abstract

We propose a method to estimate static discrete games with weak assumptions on the information available to players. We do not fully specify the information structure of the game, but allow instead for all information structures consistent with players knowing their own payoffs. To make this approach tractable we adopt as a solution concept Bayes Correlated Equilibrium (BCE) (Bergemann and Morris, 2016). We characterize the sharp identified set under BCE and unrestricted equilibrium selection, and find that in simple games with limited variation in covariates identified sets are informative. In an application, we estimate a model of entry in the Italian supermarket industry and quantify the effect of large malls on local supermarkets. Estimates and predictions differ from those obtained under more restrictive assumptions.

Sharp Test for Equilibrium Uniqueness in Discrete Games With Private Information and Common Knowledge Unobserved Heterogeneity

“…His results suggest that failing to include both private and common knowledge unobservable information may generate misleading results. More recently, Magnolfi and Roncoroni (2022) propose an estimation method applicable to games defined via an alternative equilibrium concept (Bayes Correlated Equilibrium developed by Bergemann and Morris, 2016) that allows for very weak assumptions on the information structure of the game. 8 In their empirical application, they also find that assumptions maintained on the information structure have an important impact on parameters' estimates and counterfactual predictions.…”

“…While the information structure used in Magnolfi and Roncoroni (2022) is more flexible than the one considered in the current paper, point identification of the structural parameters under Bayes Correlated Equilibrium requires player-specific regressors which are not needed to perform the test proposed in the current paper. Moreover, the identification argument using multiple equilibria in the data leveraged in Sweeting (2009), de Paula and Tang (2012), and Aradillas-López and Gandhi (2016 are based on Bayesian Nash equilibria.…”

“…Moreover, the identification argument using multiple equilibria in the data leveraged in Sweeting (2009), de Paula and Tang (2012), and Aradillas-López and Gandhi (2016 are based on Bayesian Nash equilibria. The information structure considered here is more restrictive than Magnolfi and Roncoroni (2022), but still more flexible than games of pure incomplete information.…”

Identification of firms’ beliefs in structural models of market competition

“…This solution is more robust than BNE, in the sense that it delivers all predictions compatible with BNE for any information structure within a wide class. Magnolfi and Roncoroni (2017) study inference based on the BCE solution concept. Their goal is to identify payoff parameters and they do not study the identification of beliefs.…”

Equilibrium uniqueness in entry games with private information

“…The importance of allowing for private information in entry models lies beyond the possibility of solving the multiple equilibria problem. Using complementary methodologies, Grieco (2014) and Magnolfi and Roncoroni (2023) test and reject the hypothesis that firms possess complete information at the moment of entry. Furthermore, compared to models that allow for private information, they show that assuming complete information delivers estimates that can lead to qualitatively different predictions.…”