INTERTEMPORAL PRICE DISCRIMINATION WITH STOCHASTIC VALUES RAHUL DEB†

ABSTRACT. We study the infinite-horizon pricing problem of a seller facing a buyer with single-unit demand, whose private valuation changes over time. This evolution is modeled as a stochastic shock to the buyer’s valuation arriving at a random time that is unanticipated by both the buyer and the seller. The arrival of the shock is unobserved by the seller. We show that the seller’s optimal contract with commitment consists of two prices: he will charge a low introductory price at the first instant, and a constant higher price thereafter. We also study a version of the model that allows for multiple shocks whose arrival times follow a Poisson process. It is assumed that the buyer can only make a purchase when she receives a shock. We derive the optimal contract with commitment and show that it consists of an increasing sequence of prices that converges in the limit to the highest buyer type. We show that, without commitment, the worst equilibrium for the seller is stationary, featuring a constant price over time. We characterize the set of equilibrium payoffs for the seller using this worst equilibrium as an optimal penal code