Estimation of discrete games with correlated types

In this paper, I focus on the identification and estimation of static games of incomplete information with correlated types. Instead of making the independence assumption on players' types in order to simplify the equilibrium set, I propose an approach that allows me to identify subsets of the space of covariates (i.e. publicly observed state variables in payoff functions), for which there exists a unique pure strategy Bayesian Nash equilibrium (BNE) and the equilibrium strategies are monotonic functions. Moreover, I characterize the monotonic pure strategy BNE in a simple manner and propose an estimation procedure that uses observations only from the subset of the covariate space where the game admits a unique monotonic pure strategy BNE. Furthermore, I show that the proposed estimator is <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" display="inline" altimg="urn:x-wiley:13684221:ectj12026:equation:ectj12026-math-0001" wiley:location="equation/ectj12026-math-0001.png"><msqrt><mi>n</mi></msqrt ></math>‐consistent and has a limiting normal distribution.