Optimal Mechanisms for an Auction Mediator

We consider a dynamic auction environment with a long-lived seller and short-lived buyers mediated by a third party. A mediator has incomplete information about traders' values and selects an auction mechanism to maximize her expected revenue. We characterize mediator-optimal mechanisms and show that an optimal mechanism has a simple implementation as a Vickrey auction with a reserve price where the seller pays to the mediator only a fixed percentage from the closing price.Optimal mechanism, Vickrey auction, Mediator

Efficient Auction-Based Grid Reservation using Dynamic Programming

Abstract — Auction mechanisms have been proposed as a means to efficiently and fairly schedule jobs in high-performance computing environments. The Generalized Vickrey Auction has long been known to produce efficient allocations while exposing users to truth-revealing incentives, but the algorithms used to compute its payments can be computationally intractable. In this paper we present a novel implementation of the Generalized Vickrey Auction that uses dynamic programming to schedule jobs and compute payments in pseudo-polynomial time. Additionally, we have built a version of the PBS scheduler that uses this algorithm to schedule jobs, and in this paper we present the results of our tests using this scheduler. I

Ascending auctions: some impossibility results and their resolutions with final price discounts

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments

Proving soundness of combinatorial Vickrey auctions and generating verified executable code

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable code from the formally defined auction. This removes a source of error in implementing the auction design. We intend to use formal methods to verify new auction designs. Here, our contribution is to introduce and demonstrate the use of formal methods for auction verification in the familiar setting of a well-known auction

Auctioning Securities

Treasury debt and other divisible securities are traditionally sold in either a pay-your-bid (discriminatory) auction or a uniform-price auction. We compare these auction formats with a Vickrey auction and also with two ascending-bid auctions. The Vickrey auction and the alternative ascending-bid auction (Ausubel 1996) have important theoretical advantages for sellers. In a setting without private information, these auctions achieve the maximal revenue as a unique equilibrium in dominant strategies. In contrast, the pay- your-bid, uniform-price, and standard ascending-bid auction admit a multiplicity of equilibria that yield low revenues for the seller. We show how these results extend to a setting where bidders have affiliated private information. Our results question the standard ways that securities are offered to the public.Auctions; Multi-Unit Auctions, Security Auctions, Treasury Auctions

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

Spectrum Auction Design

Spectrum auctions are used by governments to assign and price licenses for wireless communications. The standard approach is the simultaneous ascending auction, in which many related lots are auctioned simultaneously in a sequence of rounds. I analyze the strengths and weaknesses of the approach with examples from US spectrum auctions. I then present a variation, the package clock auction, adopted by the UK, which addresses many of the problems of the simultaneous ascending auction while building on its strengths. The package clock auction is a simple dynamic auction in which bidders bid on packages of lots. Most importantly, the auction allows alternative technologies that require the spectrum to be organized in different ways to compete in a technology-neutral auction. In addition, the pricing rule and information policy are carefully tailored to mitigate gaming behavior. An activity rule based on revealed preference promotes price discovery throughout the clock stage of the auction. Truthful bidding is encouraged, which simplifies bidding and improves efficiency. Experimental tests and early auctions confirm the advantages of the approach.Auctions, spectrum auctions, market design, package auction, clock auction, combinatorial auction