Equilibrium models of multiple-object auctions

Citation

Palfrey, Thomas R. (1981) Equilibrium models of multiple-object auctions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4MB5-N246. https://resolver.caltech.edu/CaltechETD:etd-06122008-082054

Abstract

This dissertation uses two different game-theoretic models to explore properties of equilibria in multiple-object auctions and presents the results of an empirical test of one of them. The first chapter surveys the most important contributions to auction and bidding theory, discusses some questions which have not yet been answered satisfactorily and outlines some of the specific problems which must be addressed when studying multiple-object auctions as opposed to single-object auctions. Chapter two examines the existence and characterization of pure strategy Nash equilibria in multiple-object auction games in which buyers face a binding constraint on exposure. There are five major results. First, symmetric Nash equilibria exist if and only if there are two or less buyers and two or less objects. Second, a Nash equilibrium may not exist if the seller sets a positive reservation bid. Third, asymmetric solutions to symmetrically parametrized games typically involve "high-low" strategies: buyers submit positive bids only on some restricted subset of the objects. Fourth, Nash equilibria typically generate zero "profits" to the buyers. Fifth, when asymmetric solutions exist and the buyers are identical, these solutions are never unique. Chapter three examines the bundling decisions by a multiproduct monopolist with incomplete information about demand. Previously the bundling problem has been analyzed only in a world of perfect and complete information in which the monopolist uses a standard take-it-or-leave-it pricing scheme. The model in chapter three shows that tied-in sales are sometimes ex ante optimal under a reasonable set of assumptions about a world in which there are no production economies or diseconomies and no demand interdependencies. A number of additional results were obtained deriving general sufficient conditions for buyers to prefer bundling, as well as conditions under which bundling is optimal in terms of maximizing expected consumer plus producer surplus. Chapter four reports the results of an empirical examination of the predictions made in chapter three. Testable hypotheses were developed in that chapter which addressed questions about seller revenues, market efficiency, buyer behavior and distributional consequences of a monopolistic seller's bundling decision in multiple object auctions. The data provide strong support for these theoretically-based hypotheses.

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