Rate of Price Discovery in Iterative Combinatorial Auctions

We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class, bounding the number of auction rounds needed to reach clearing prices. Our analysis allows for a variety of pricing schemes, including item, bundle, and polynomial pricing, and the respective convergence rates confirm that more expressive pricing schemes come at the cost of slower convergence. We consider two models of bidder behavior. In the first model, bidders behave stochastically according to a random utility model, which includes standard best-response bidding as a special case. In the second model, bidders behave arbitrarily (even adversarially), and meaningful convergence relies on properly designed activity rules

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

On the Communication Requirements of Verifying the VCG Outcome

We consider the amount of communication required to verify the outcome of the Vickrey-Clarke-Groves (VCG) mechanism: an efficient allocation together with incentivizing VCG payments. We compare this to the communication required to verify the efficient decision rule alone, to assess the overhead imposed by VCG payments. Our characterizations are obtained by leveraging a connection between the VCG outcome and a price equilibrium concept known as universal competitive equilibrium. We consider four related environments within a common framework: the classic single-item setting, the multi-unit setting with decreasing marginal values, the classic assignment problem with unit-demand valuations, and the multi-unit assignment problem with substitutes valuations. We find that the single-unit settings have zero overhead, whereas the multi-unit settings can have significant positive overhead. With multiple units, the naïve VCG protocol that runs several efficient protocols in sequence (one with all agents, and ones with an agent removed, for each agent) is asymptotically optimal for several parameter settings of the number of agents, commodities, and units.Engineering and Applied Science

A Modular Framework for Iterative Combinatorial Auctions

We describe a modular elicitation framework for iterative combinatorial auctions. The framework includes proxy agents, each of which can adopt an individualized bidding language to represent partial value information of a bidder. The framework leverages algorithms from query learning to elicit value information via bids as the auction progresses. The approach reduces the multi-agent elicitation problem to isolated, single-agent learning problems, with competitive equilibrium prices used to facilitate auction clearing even without complete learning.Engineering and Applied Science

Applying Learning Algorithms to Preference Elicitation

We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms perform a polynomial number of queries. We also give conditions under which the resulting algorithms have polynomial communication. Our conversion procedure allows us to generate combinatorial auction protocols from learning algorithms for polynomials, monotone DNF, and linear-threshold functions. In particular, we obtain an algorithm that elicits XOR bids with polynomial communication.Engineering and Applied Science

More on the Power of Demand Queries in Combinatorial Auctions: Learning Atomic Languages and Handling Incentives

Query learning models from computational learning theory (CLT) can be adopted to perform elicitation in combinatorial auctions. Indeed, a recent elicitation framework demonstrated that the equivalence queries of CLT can be usefully simulated with price-based demand queries. In this paper, we validate the flexibility of this framework by defining a learning algorithm for atomic bidding languages, a class that includes XOR and OR. We also handle incentives, characterizing the communication requirements of the Vickrey-Clarke-Groves outcome rule. This motivates an extension to the earlier learning framework that brings truthful responses to queries into an equilibrium.Engineering and Applied Science

An Expressive Auction Design for Online Display Advertising

We propose an expressive auction design that allows advertisers to specify the kinds of demographics and websites they wish to target within an advertising network. The design allows the network to differentiate impressions according to relevant attributes (e.g., geographic location of the user, topic of the webpage). Advertisers can place bids for different kinds of impressions according to their attributes, and can also specify volume constraints to control exposure. The novelty of the design is a bidding language that admits scalable allocation and pricing algorithms. We discuss the incentive properties of different pricing approaches. We also propose a bidder feedback mechanism to mitigate the complexity of expressive bidding.Engineering and Applied Science