Quantile Analysis of "Hazard-Rate" Game Models

This paper consists of an econometric analysis of a broad class of games of incomplete information. In these games, a player’s action depends both on her unobservable characteristic (the private information), as well as on the ratio of the distribution of the unobservable characteristic and its density function (which we call the "hazard-rate"). The goal is to use data on players’actions to recover the distribution of private information. We show that the structural parameter (the distribution of the unobservable characteristic) can be related to the reduced form parameter (the distribution of the data) through a quantile relation that avoids the inversion of the players’ strategy function. We estimate non-parametrically the density of the unobserved variables and we show that this is the solution of a well-posed inverse problem. Moreover, we prove that the density of the private information is estimated at a Vpn speed of convergence. Our results have several policy applications, including better design of auctions and public good contracts.