Learning optimization models in the presence of unknown relations

In a sequential auction with multiple bidding agents, it is highly challenging to determine the ordering of the items to sell in order to maximize the revenue due to the fact that the autonomy and private information of the agents heavily influence the outcome of the auction. The main contribution of this paper is two-fold. First, we demonstrate how to apply machine learning techniques to solve the optimal ordering problem in sequential auctions. We learn regression models from historical auctions, which are subsequently used to predict the expected value of orderings for new auctions. Given the learned models, we propose two types of optimization methods: a black-box best-first search approach, and a novel white-box approach that maps learned models to integer linear programs (ILP) which can then be solved by any ILP-solver. Although the studied auction design problem is hard, our proposed optimization methods obtain good orderings with high revenues. Our second main contribution is the insight that the internal structure of regression models can be efficiently evaluated inside an ILP solver for optimization purposes. To this end, we provide efficient encodings of regression trees and linear regression models as ILP constraints. This new way of using learned models for optimization is promising. As the experimental results show, it significantly outperforms the black-box best-first search in nearly all settings.Comment: 37 pages. Working pape

Putting auction theory to work : the simultaneous ascending auction

The"simultaneous ascending auction"was first introduced in 1994 to sell licenses to use bands of radio spectrum in the United States. Much of the attention devoted to the auction came from its role in reducing federal regulation of the radio spectrum and allowing market values, rather than administrative fiat, to determine who would use the spectrum resource. Several parts of economic theory proved helpful in designing the rules for simultaneous ascending auction and in thinking about how the design might be improved and adapted for new applications. After briefly reviewing the major rules of the auction in section 2, the author turns in section 3 to an analysis based on tatonnement theory, which regards the auction as a mechanism for discovering an efficient allocation and its supporting prices. The analysis reveals a fundamental difference between situations in which the licenses are mutual substitutes and others in which the same licenses are sometimes substitutes and sometimes complements. Section 4 is a selective account of some applications of game theory to evaluating the simultaneous ascending auction design for spectrum sales. Results like those reported in section 3 have led to renewed interest in auctions in which bids for license packages are permitted. In section 5, the author uses game theory to analyze the biases in a leading proposal for dynamic combinatorial bidding. Section 6 briefly answers two additional questions that economists often ask about auction design: If trading of licenses after the auction is allowed, why does the auction form matter at all for promoting efficient license assignments? Holding fixed the quantity of licenses to be sold, how sharp is the conflict between the objectives of assigning licenses efficiently and obtaining maximum revenue? Section 7 concludes.Economic Theory&Research,International Terrorism&Counterterrorism,Markets and Market Access,Environmental Economics&Policies,Labor Policies,Markets and Market Access,Access to Markets,Economic Theory&Research,Environmental Economics&Policies,International Terrorism&Counterterrorism

Online Auctions

The economic literature on online auctions is rapidly growing because of the enormous amount of freely available field data. Moreover, numerous innovations in auction-design features on platforms such as eBay have created excellent research opportunities. In this article, we survey the theoretical, empirical, and experimental research on bidder strategies (including the timing of bids and winner's-curse effects) and seller strategies (including reserve-price policies and the use of buy-now options) in online auctions, as well as some of the literature dealing with online-auction design (including stopping rules and multi-object pricing rules).

Sequential auction and auction design

Often an auction designer has the option of selling, or purchasing, those lots available in one auction or a sequence of auctions. In addition, bidder opportunities will not be static, in part due to arrival of information, but also because bidders can face deadlines for making decisions. This paper examines the optimal decision about how to divide what is available over time.sequential auctions

Bidding efficiently in Simultaneous Ascending Auctions with budget and eligibility constraints using Simultaneous Move Monte Carlo Tree Search

For decades, Simultaneous Ascending Auction (SAA) has been the most popular mechanism used for spectrum auctions. It has recently been employed by many countries for the allocation of 5G licences. Although SAA presents relatively simple rules, it induces a complex strategical game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in a SAA, establishing an efficient bidding strategy is crucial. In this work, we model the auction as a $n$-player simultaneous move game with complete information and propose the first efficient bidding algorithm that tackles simultaneously its four main strategical issues: the $\textit{exposure problem}$, the $\textit{own price effect}$, $\textit{budget constraints}$ and the $\textit{eligibility management problem}$. Our solution, called $SMS^\alpha$, is based on Simultaneous Move Monte Carlo Tree Search (SM-MCTS) and relies on a new method for the prediction of closing prices. By introducing scalarised rewards in $SMS^\alpha$, we give the possibility to bidders to define their own level of risk-aversion. Through extensive numerical experiments on instances of realistic size, we show that $SMS^\alpha$ largely outperforms state-of-the-art algorithms, notably by achieving higher expected utility while taking less risks.Comment: 14 pages, 10 figures, The paper has been submitted to IEEE journal for possible publicatio

Multiple Items, Ascending Price Auctions: An Experimental Examination of Alternative Auction Sequences

The paper investigates the revenue and efficiency of different ascending price auction architectures for the sale of three items and five bidders. Four architectures are studied: two different sequences of single item auctions, simultaneous auctions with a common countdown clock, and simultaneous auctions with item specific countdown clocks. A countdown clock measures the time until the auction closes but resets with each new bid. The environment contains independent private values, no uncertainty about own preferences, no information about other’s preferences, and a one unit budget constraint. The Nash equilibrium best response with straight forward bidding fits both dynamic and outcome data well. When non-unique Nash equilibria exist as in the case of simultaneous markets with a common clock, the social value maximizing Nash equilibrium emerges as the equilibrium selection. Both total revenue and efficiencies depend on the architecture as predicted by the Nash model, with the exception of the independent clocks architecture, which performs poorly on all dimensions