Fast Iterative Combinatorial Auctions via Bayesian Learning

Iterative combinatorial auctions (CAs) are often used in multi-billion dollar domains like spectrum auctions, and speed of convergence is one of the crucial factors behind the choice of a specific design for practical applications. To achieve fast convergence, current CAs require careful tuning of the price update rule to balance convergence speed and allocative efficiency. Brero and Lahaie (2018) recently introduced a Bayesian iterative auction design for settings with single-minded bidders. The Bayesian approach allowed them to incorporate prior knowledge into the price update algorithm, reducing the number of rounds to convergence with minimal parameter tuning. In this paper, we generalize their work to settings with no restrictions on bidder valuations. We introduce a new Bayesian CA design for this general setting which uses Monte Carlo Expectation Maximization to update prices at each round of the auction. We evaluate our approach via simulations on CATS instances. Our results show that our Bayesian CA outperforms even a highly optimized benchmark in terms of clearing percentage and convergence speed.Comment: 9 pages, 2 figures, AAAI-1

The performance of deferred-acceptance auctions

Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and can be implemented by ascending-clock auctions. Neither forward greedy mechanisms nor the VCG mechanism generally possess any of these additional incentive properties. The goal of this paper is to initiate the study of deferred-acceptance auctions from an approximation standpoint. We study what fraction of the optimal social welfare can be guaranteed by these auctions in two canonical problems, knapsack auctions and combinatorial auctions with single-minded bidders. For knapsack auctions, we prove a separation between deferred-acceptance auctions and arbitrary dominant-strategy incentive-compatible mechanisms. For combinatorial auctions with single-minded bidders, we design novel polynomial-time mechanisms that achieve the best of both worlds: the incentive guarantees of a deferred-acceptance auction, and approximation guarantees close to the best possible

Modularity and greed in double auctions

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer). We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction. Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers

Energy Procurement through E-auctions

Tato práce se zabývá nákupem energií prostřednictvím e-aukcí. Zkoumaným problémem bylo zjistit jaký vliv má cena na burze na výslednou cenu aukce, jaký vliv má načasování aukce a jaká je marže dodavatelů. Problém byl zkoumán pomocí regresní analýzy dat získaných od společnosti zabývající se aukcemi a doplněná o data z burzy PXE. Z analýzy dat vyplynulo, že závislost mezi cenou na burze a výherní cenou aukce existuje. Dále, že načasování aukce je podstatné především s ohledem na vývoj cen na burze a v neposlední řadě, že marže dodavatelů u smluv na 12 a 24 měsíců není příliš rozdílná a je ovlivněna především počtem dražených MWh. Výsledným doporučením pro malé a střední společnosti je tedy nakupovat elektrickou energii prostřednictvím společných aukcí s dalšími společnostmi a cenu fixovat na 12 nebo 24 měsíců v závislosti na předpokládaném vývoji cen elektrické energie na burze.This paper deals with the purchase of energy through e-auctions. The researched issue was to determine the influence of the stock market price on the final price of the auction, the influence of the timing at auction and what is the margin of suppliers. The problem was studied using regression analysis of data obtained from the companies dealing with auctions and supplemented by data from PXE. The analysis of the data showed that there is a connection between the quoted market price auction and winning price exists. Furthermore, the timing of the auction is important especially with regard to developments in prices on the stock exchange and, finally, that the margins of suppliers for contracts for 12 and 24 months is not much different and is influenced mainly by the number of auctioned MWh. The resulting recommendations for small and medium-sized companies is therefore purchase of electricity through public auctions and other companies to fix the price for 12 or 24 months, depending on the expected development of electricity prices on the stock exchange.116 - Katedra marketingu a obchoduvýborn

Optimizing prices in descending clock auctions

A descending (multi-item) clock auction (DCA) is a mechanism for buying items from multiple potential sellers. In the DCA, bidder-specific prices are decremented over the course of the auction. In each round, each bidder might accept or decline his offer price. Accepting means the bidder is willing to sell at that price. Rejecting means the bidder will not sell at that price or a lower price. DCAs have been proposed as the method for procuring spectrum from existing holders in the FCC's imminent incentive auctions so spectrum can be repurposed to higher-value uses. However, the DCA design has lacked a way to determine the prices to offer the bidders in each round. This is a recognized, important, and timely problem.We present, to our knowledge, the first techniques for this. We develop a percentile-based approach which provides a means to naturally reduce the offer prices to the bidders through the bidding rounds. We also develop an optimization model for setting prices so as to minimize expected payment while stochastically satisfying the feasibility constraint. (The DCA has a final adjustment round that obtains feasibility after feasibility has been lost in the final round of the main DCA.) We prove attractive properties of this, such as symmetry and monotonicity. We develop computational methods for solving the model. (We also develop optimization models with recourse, but they are not computationally practical.) We present experiments both on the homogeneous items case and the case of FCC incentive auctions, where we use real interference constraint data to get a fully faithful model of feasibility. An unexpected paradox about DCAs is that sometimes when the number of rounds allowed increases, the final payment increases. We provide an explanation for this