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Discrete approximation of continuous allocation mechanisms

Citation

Yu, Jin (1999) Discrete approximation of continuous allocation mechanisms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02052008-141952

Abstract

This dissertation discusses two allocation mechanisms through which prices are set in markets.

The first chapter presents theories on discrete-bid auctions. In particular, we focus on four common auction institutions: the sealed-bid first-price auction, the sealed- bid second-price auction, the English auction and the Dutch auction, in a single-object, independent-private-value setting in which bids can only be multiples of some fixed increment. Two different models of English auction, the pay-your-bid and the penultimate-bid English auction are introduced. It is shown that when bids are discrete, second-price auctions and English auctions are no longer dominance solvable as bidding games. Bidding is more aggressive in the penultimate-bid English auction than that in the pay-your-bid English auction. Nevertheless, first-price auctions and Dutch auctions are still strategically equivalent. The equivalence of expected revenues in the continuous case breaks down when bids are discrete. As the number of bidders participating in the auction increases, auctions in which the winner pays the next highest bid (second-price auctions and penultimate-bid English auctions) are more likely to yield higher expected revenues than auctions in which the winner pays his own bid (first-price auctions and pay-your-bid English auctions). The probability of tie in discrete-bid auctions is strictly positive and hence resulting allocations can be Pareto inefficient.

Chapter 2 reports the laboratory observations of bidders' behavior in the pay your-bid and penultimate-bid English auctions. Results of six experiments show that theories developed in the first chapter in general perform very well in predicting the bidding behavior and the price range. However, observations of bidding that is significantly lower than what has been predicted by theory do exist in experiments with small increment. Two possible explanations are discussed.

Chapter 3 discusses a situation in which a monopolist seeks to sell a quality-differentiated spectrum of products of the same generic type to consumers of different characteristics that he cannot observe. The main difference between this framework and the previous literature is that there is a fixed set-up cost of each type of product. The presence of set-up cost makes it impossible for the monopolist to fully separate different types of consumers. The main purpose of this paper is to discuss the monopolist's profit maximization problem and characterize the optimal solution. It is shown that the lowest type in the consumer group consuming the highest quality level would be served efficiently in that the consumer's marginal rate of substitution between price and quality equals that of the monopolist. All other consumers will be served inefficiently and quality distortion takes the form of degradation. The monopolist's profit margin increases with the quality level and an upward shift of the distribution of consumer preference brings higher profit to the monopolist.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:auction; discrete mechanism design; monopoly
Degree Grantor:California Institute of Technology
Division:Humanities and Social Sciences
Major Option:Social Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ledyard, John O.
Thesis Committee:
  • Ledyard, John O. (chair)
  • Border, Kim C.
  • Palfrey, Thomas R.
Defense Date:17 August 1998
Record Number:CaltechETD:etd-02052008-141952
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-02052008-141952
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:510
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:05 Feb 2008
Last Modified:26 Dec 2012 02:30

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