Automated Mechanism Design

Mechanisms design has traditionally been a manual endeavor. In 2002, Conitzer and Sandholm introduced the automated mechanism design (AMD) approach, where the mechanism is computationally created for the specific problem instance at hand. This has several advantages: 1) it can yield better mechanisms than the ones known to date, 2) it applies beyond the problem classes studied manually to date, 3) it can circumvent seminal economic impossibility results that hold for classes of problems but not all instances, and 4) it shifts the burden of design from man to machine. In this talk I will overview our results on AMD to date. I will cover problem representations and the computational complexity of different variants of the design problem. Initial applications include revenue-maximizing combinatorial auctions and (combinatorial) public goods problems. Algorithms for AMD will be discussed. To reduce the computational complexity of designing optimal combinatorial auctions, I introduce an incentive compatible, individually rational subfamily called Virtual Valuations Combinatorial Auctions. The auction mechanism\u27s revenue can be boosted (started, for example, from the VCG) by hill-climbing in this subspace. I will also present computational complexity and communication complexity results that motivate multi-stage and non-truth-promoting mechanisms. Finally, I present our first steps toward automatically designing multi-stage mechanisms

Limitations of Incentive Compatibility on Discrete Type Spaces

In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set $T$ of discrete types can be extended to the convex hull of $T$. Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.Comment: 11 pages, 2 figures, to be published in Thirty-Fourth AAAI Conference on Artificial Intelligenc

A General Theory of Sample Complexity for Multi-Item Profit Maximization

The design of profit-maximizing multi-item mechanisms is a notoriously challenging problem with tremendous real-world impact. The mechanism designer's goal is to field a mechanism with high expected profit on the distribution over buyers' values. Unfortunately, if the set of mechanisms he optimizes over is complex, a mechanism may have high empirical profit over a small set of samples but low expected profit. This raises the question, how many samples are sufficient to ensure that the empirically optimal mechanism is nearly optimal in expectation? We uncover structure shared by a myriad of pricing, auction, and lottery mechanisms that allows us to prove strong sample complexity bounds: for any set of buyers' values, profit is a piecewise linear function of the mechanism's parameters. We prove new bounds for mechanism classes not yet studied in the sample-based mechanism design literature and match or improve over the best known guarantees for many classes. The profit functions we study are significantly different from well-understood functions in machine learning, so our analysis requires a sharp understanding of the interplay between mechanism parameters and buyer values. We strengthen our main results with data-dependent bounds when the distribution over buyers' values is "well-behaved." Finally, we investigate a fundamental tradeoff in sample-based mechanism design: complex mechanisms often have higher profit than simple mechanisms, but more samples are required to ensure that empirical and expected profit are close. We provide techniques for optimizing this tradeoff

Instantiating the contingent bids model of truthful interdependent value auctions

(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Ito, Takayuki, and David C. Parkes. 2006. Instantiating the contingent bids model of truthful interdependent value auctions. I

Methods for Boosting Revenue in Combinatorial Auctions

Computer Science Departmen

Methods for Boosting Revenue in Combinatorial Auctions

We study the recognized open problem of designing revenuemaximizing combinatorial auctions. It is unsolved even for two bidders and two items for sale. Rather than pursuing the pure economic approach of attempting to characterize the optimal auction, we explore techniques for automatically modifying existing mechanisms in a way that increase expected revenue. We introduce a general family of auctions, based on bidder weighting and allocation boosting, which we call virtual valuations combinatorial auctions (VVCA). All auctions in the family are based on the Vickrey-Clarke-Groves (VCG) mechanism, executed on virtual valuations that are linear transformations of the bidders' real valuations. The restriction to linear transformations is motivated by incentive compatibility. The auction family is parameterized by the coefficients in the linear transformations. The proble