Semiparametric Estimation of Signaling Games

This paper studies an econometric modeling of a signaling game with two players where one player has one of two types. In particular, we develop an estimation strategy that identies the payos structure and the distribution of types from data of observed actions. We can achieve uniqueness of equilibrium using a renement, which enables us to identify the parameters of interest. In the game, we consider non-strategic public signals about the types. Because the mixing distribution of these signals is nonparametrically specified, we propose to estimate the model using a sieve conditional MLE. We achieve the consistency and the asymptotic normality of the structural parameters estimates. As an alternative, we allow for the possibility of multiple equilibria, without using an equilibrium selection rule. As a consequence, we adopt a set inference allowing for multiplicity of equilibria.