Advertising and Sealed Bid Auctions in a Transshipment Game

Gerald L. Thompson
Graduate School of Industrial Administration, Carnegie Mellon University
gt04+@andrew.cmu.edu

Sten Thore
The IC Institute, The University of Texas at Austin
stent@icc.utexas.edu

Abstract

In an earlier paper (Thompson and Thore, 1995), we suggested employing the sealed-bid auction as a format for modelling the marketing of a wide range of heterogeneous products, including the marketing of most brand names. The formation of prices in such markets is described as if it resulted from an actual sealed-bid auction, with buyers inspecting the goods offered for sale by the various manufacturers, and making sealed bids which later are opened by a hypothetical auctioneer. While surely putative, this model nevertheless seems superior to the standard assumptions of perfect competition where a homogeneous commodity is transacted and all buyers offer identical prices.

Extending the use of the sealed bid auction, we here consider cases where the manufacturers or distributors promote their sales by advertising. While the quantity demanded by each customer is fixed and given, his bids on the various brands is determined by the advertising and other promotional efforts. The bid response function for each consumer is supposed to be given and known. The preceding vertical production and distribution chain, from the supply of raw materials and primary commodities, via the successive processing, manufacturing and distribution of the product is described as a transshipment game.

We formulate a complementarity model that in one step solves this entire logistics system, including the possible formation of coalitions between suppliers and/or distributors, the market prices of the various brands, the optimal distribution of the product, and the bids of the consumers. A numerical example is provided and the solution routine is discussed.