Supplement for Identication and Estimation of Games with Incomplete Information Using Excluded Regressors"

This online supplement to Lewbel and Tang (2014) provides proofs and additional results. Section A provides results regarding existence of required sets of states and assumed support conditions. Section B provides further discussion and formal derivations of our asymptotic results, and Section C gives the proof of Theorem 3. This section provides further primitive conditions on model elements that are su¢ cient for some of the identifying conditions in the text. These include the existence of a non-degenerate and non-singular (n.d.s.) set for a given ~ x; and the large support condition in A4 and A4'. In Section 3.2 of Lewbel and Tang (2014), we give conditions under which there exists a n.d.s. set for a generic vector of non-excluded regressors ~ x. Here in this section we give stronger conditions that ensure there exists a n.d.s. set ! where the equilibrium is unique. This is useful for the identi…cation strategy discussed in Section 7.1 of Lewbel and Tang (2014). Consider a game with N = 2 (with players denoted by 1 and 2) and h i (D j) = D j for i = 1; 2 and j = 3 i. To begin with, we give conditions under which the game admits a unique equilibrium at a generic state x. Let p (p 1 ; p 2) and de…ne: