Sealed bid second price auctions with discrete bids

A single item is sold to two bidders by way of a sealed bid second price auction in which bids are restricted to a set of discrete values. Restricting attention to symmetric pure strategy behavior on the part of bidders, a unique equilibrium exists. When following these equilibrium strategies bidders may bid strictly above or below their valuation, implying that the item may be awarded to a bidder other than the high valuation bidder. In an auction with two acceptable bids, the expected revenue of the seller may be maximized by a high bid level not equal to the highest possible bidder valuation and may exceed the expected revenue from an analogous second price auction with continuous bidding (and no reserve price). With three acceptable bids, a revenue maximizing seller may choose unevenly spaced bids. With an arbitrary number of evenly spaced bids, as the number of acceptable bids is increased, the expected revenue of the seller and the probability of ex post inefficiency both may either increase or decrease

Optimal Design Of English Auctions With Discrete Bid Levels

This paper considers a form of ascending price English auction widely used in both live and online auctions. This discrete bid auction requires that the bidders submit bids at predetermined discrete bid levels, and thus, there exists a minimal increment by which the bid price may be raised. In contrast, the academic literature of optimal auction design deals almost solely with continuous bid auctions. As a result, there is little practical guidance as to how an auctioneer, seeking to maximize its revenue, should determine the number and value of these discrete bid levels, and it is this omission that is addressed here. To this end, a model of a discrete bid auction from the literature is considered, and an expression for the expected revenue of this auction is derived. This expression is used to determine both numerical and analytical solutions for the optimal bid levels, and uniform and exponential bidder’s valuation distributions are compared. Finally, the limiting case where the number of discrete bid levels is large is considered. An analytical expression for the distribution of the optimal discrete bid levels is derived, and an intuitive understanding of how this distribution maximizes the revenue of the auction is developed

Applying revenue management to agent-based transportation planning

We consider a multi-company, less-than-truckload, dynamic VRP based on the concept of multi-agent systems. We focus on the intelligence of one vehicle agent and especially on its bidding strategy. We address the problem how to price loads that are offered in real-time such that available capacity is used in the most profitable way taking into account possible future revenues. We develop methods to price loads dynamically based on revenue management concepts.\ud We consider a one leg problem, i.e., a vehicle travels from i to j and can wait at most τ time units in which it can get additional loads from i to j. We develop a DP to price loads given a certain amount of remaining capacity and an expected number of auctions in the time-to-go. Because a DP might be impractical if parameters change frequently and bids has to be determined in real-time, we derived two approximations to speed up calculations. The performance of these approximations are compared with the performance of the DP. Besides we introduce a new measure to calculate the average vehicle utilisation in consolidated shipments. This measure can be calculated based on a limited amount of data and gives an indication of the efficiency of schedules and the performance of vehicles

Why Every Economist Should Learn Some Auction Theory

This is an Invited paper for the World Congress of the Econometric Society held in Seattle in August 2000. We discuss the strong connections between auction theory and "standard" economic theory, and argue that auction-theoretic tools and intuitions can provide useful arguments and insights in a broad range of mainstream economic settings that do not, at first sight, look like auctions. We also discuss some more obvious applications, especially to industrial organization.Auctions, Bidding, Auction Theory, Private Values, Common Values, Mechanism Design, Litigation, Stock Markets, Queues, Financial Crashes, Brand Loyalty, War of Attrition, Bertrand, Perfect Competition, E-Commerce, Spectrum Auctions, Treasury Auctions, Electricity

An Investigation Report on Auction Mechanism Design

Auctions are markets with strict regulations governing the information available to traders in the market and the possible actions they can take. Since well designed auctions achieve desirable economic outcomes, they have been widely used in solving real-world optimization problems, and in structuring stock or futures exchanges. Auctions also provide a very valuable testing-ground for economic theory, and they play an important role in computer-based control systems. Auction mechanism design aims to manipulate the rules of an auction in order to achieve specific goals. Economists traditionally use mathematical methods, mainly game theory, to analyze auctions and design new auction forms. However, due to the high complexity of auctions, the mathematical models are typically simplified to obtain results, and this makes it difficult to apply results derived from such models to market environments in the real world. As a result, researchers are turning to empirical approaches. This report aims to survey the theoretical and empirical approaches to designing auction mechanisms and trading strategies with more weights on empirical ones, and build the foundation for further research in the field

Spectrum Auctions

Auctions have emerged as the primary means of assigning spectrum licenses to companies wishing to provide wireless communication services. Since July 1994, the Federal Communications Commission (FCC) has conducted 33 spectrum auctions, assigning thousands of licenses to hundreds of firms. Countries throughout the world are conducting similar auctions. I review the current state of spectrum auctions. Both the design and performance of these auctions are addressed.Auctions, Spectrum Auctions, Multiple Item Auctions

The German UMTS Design: Insights From Multi-Object Auction Theory

We briefly survey several insights about value and revenue maximization in multi-object auctions and apply them to the German (and Austrian) UMTS auction. In particular, we discuss in detail the exposure probelm that caused firms in Germany to pay almost Euro 20 billion for nothing.

Fraction auctions: the tradeoff between effciency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [13] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time.operations research and management science;