A class Hotelling model for sequential auctions of close substitutes

Abstract

Against the background of supply chains, this paper constructs a class Hotelling model to describe and explore sequential auctions of close substitutes with slightly more general associated valuations. In this generalized model, both close substitutes and bidders are hypothetically distributed in the interval [0, 1], types of bidders are continuous, and each bidder's valuations for close substitutes are not independent. And with the aid of this model, equilibriums are explored and efficiencies of the auctions are analyzed under second-price sealed-bid auction formats. Further considering two typical information policies, we investigate some concrete bids and revenues of the efficient sequential auctions while bidders' valuations are linear functions of distances between them and close substitutes. Results show that efficiencies of the sequential auctions are conditional, and influences of information policies on revenues of the auctions are related to both numbers of bidders and locations of items.