Estimation of Discrete Games with Weak Assumptions on Information (with Camilla Roncoroni)

We propose a new method to estimate the distribution of preferences when behavior is described by equilibrium play in static discrete games, while maintaining weak assumptions on the information available to players. Structural game theoretic models are useful to quantify the impact of policy on the decisions of strategic firms, but require assumptions on primitives that are unknown to the researcher. We focus on assumptions about the information available to players, since these are key in determining model’s predictions, and misspecification of features of the information structure could result in biased estimates of the parameters of interest.

In contrast to the existing literature, we do not fully specify the information structure of the game. Instead, we allow for all information structures consistent with the assumptions that players know (i) their own payoffs, (ii) the distribution of opponents’ payoffs, and (iii) parameters and observable covariates. Our object of interest is the set of all parameters that are identified if predictions are generated by any Bayes Nash Equilibrium (BNE), given an admissible information structure. As a consequence, our model nests the standard assumptions, adopted in the existing literature, of complete information and perfectly private information. We make this approach tractable by adopting a weaker solution concept that captures the predictions of equilibrium behavior for all possible information structures: Bayes Correlated Equilibrium (BCE), as defined in Bergemann and Morris (2013, 2015).

We characterize the (sharp) identified set obtained under the assumption of BCE behavior, and show that it contains all and only the parameters that are compatible with the data and with a BNE given an admissible information structure. We show that entry games with BCE behavior are point identified under the same assumptions that guarantee point identification in models that restrict the information structure. Moreover, identified sets are narrow enough to be informative in simple examples of entry games with modest levels of variation in observable covariates.

The robustness achieved by our method is desirable, because misspecification of the information structure can result in biased estimates. In an application, we present quantitative evaluations of the effect of the presence of large shopping centers on competition in the Italian supermarket industry, by estimating a model of static entry. We estimate our model and compare the results with estimates obtained under the assumption of complete information. The two methods yield different parameter estimates and different market structure implications of a policy that would prevent large shopping centers from operating in small geographical markets.