Economic Theory Seminar - Ellen Muir (Harvard)

Title: Optimal Hotelling Auctions (joint with Simon Loertscher)

Abstract: We derive the optimal selling mechanism for a seller who offers differentiated products located at opposite ends of the Hotelling line. The agents have linear transportation costs and draw their locations independently from commonly known distributions satisfying Myerson's regularity condition. We assume that the agents' gross valuation are sufficiently large so that full market coverage is optimal. We show that when the seller faces a single buyer, the seller optimally randomizes between the two goods when the agent is located in some interior interval. With multiple agents, the optimal selling mechanisms still involves random allocation, but the subset of types for whom randomization occurs in equilibrium varies with the numbers of agents, the number of goods at each location and the agents' distributions.