First-Price Sealed-Bid Auctions with Secret Reservation Prices

In this paper we consider a first-price sealed bid auction with a secret reservation price. Such auctions are used frequently in France to sell timber. Within the independent private values paradigm, we show that the equilibrium strategy of the seller is to choose a reservation price equal to his private value. We characterize the symmetric Bayesian equilibrium strategy for the buyers as the solution of a differential equation. We also show that a strategy of public reservation price is better for the seller than a strategy of secret reservation price. To evaluate the expected gain for the seller from moving from a secret to the optimal public reservation price, we estimate the model using data from an actual auction of timber. First, we solve the problem of identification of the underlying distributions of private values. Then we propose a two-step structural nonparametric estimation method to shed some lights on the shapes of these distributions. This is used to formulate and estimate a parsimonious and structural parametric model that reproduces the salient features of our nonparametric analysis.