An Agent Based Market Design Methodology for Combinatorial Auctions

Auction mechanisms have attracted a great deal of interest and have been used in diverse e-marketplaces. In particular, combinatorial auctions have the potential to play an important role in electronic transactions. Therefore, diverse combinatorial auction market types have been proposed to satisfy market needs. These combinatorial auction types have diverse market characteristics, which require an effective market design approach. This study proposes a comprehensive and systematic market design methodology for combinatorial auctions based on three phases: market architecture design, auction rule design, and winner determination design. A market architecture design is for designing market architecture types by Backward Chain Reasoning. Auction rules design is to design transaction rules for auctions. The specific auction process type is identified by the Backward Chain Reasoning process. Winner determination design is about determining the decision model for selecting optimal bids and auctioneers. Optimization models are identified by Forward Chain Reasoning. Also, we propose an agent based combinatorial auction market design system using Backward and Forward Chain Reasoning. Then we illustrate a design process for the general n-bilateral combinatorial auction market. This study serves as a guideline for practical implementation of combinatorial auction markets design.Combinatorial Auction, Market Design Methodology, Market Architecture Design, Auction Rule Design, Winner Determination Design, Agent-Based System

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 Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditional optimal mechanism design approach is ill-suited --- either because it makes overly strong assumptions, or because it advocates overly complex designs. The thesis of this paper is that approximately optimal mechanisms allow us to reason about fundamental questions that seem out of reach of the traditional theory. This survey has three main parts. The first part describes the approximately optimal mechanism design paradigm --- how it works, and what we aim to learn by applying it. The second and third parts of the survey cover two case studies, where we instantiate the general design paradigm to investigate two basic questions. In the first example, we consider revenue maximization in a single-item auction with heterogeneous bidders. Our goal is to understand if complexity --- in the sense of detailed distributional knowledge --- is an essential feature of good auctions for this problem, or alternatively if there are simpler auctions that are near-optimal. The second example considers welfare maximization with multiple items. Our goal here is similar in spirit: when is complexity --- in the form of high-dimensional bid spaces --- an essential feature of every auction that guarantees reasonable welfare? Are there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on Economics and Computation (EC), June 201