arXiv subjects

Benjamin Lubin

Publications and source records attributed to Benjamin Lubin.

10 recordsLinked to original sources

arXiv2025

Iterative Vickrey Auctions via Linear Programming

Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we derive iterative Vickrey auctions that maintain a single price path, eliminating the overhead and incentive problems associated with multiple price paths used solely for payment calculations. We demonstrate the versatility of our method by developing a novel iterative Vickrey auction for the multi-unit setting and an iterative variant of the Product-Mix auction. The resulting auctions combine the transparency of iterative price discovery with the efficiency and incentive properties of the VCG mechanism.

cs.GT↗

arXiv2025

Pricing Valid Cuts for Price-Match Equilibria

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We thus provide a method for converting a CA problem that admits only non-anonymous, nonlinear bundle prices into one that admits anonymous linear prices over the augmented item space, forestalling ex-post bidder complaints about opaque and strongly discriminatory pricing. To this end, we introduce a refinement of the Walrasian equilibrium which we call a "price-match equilibrium" (PME) in which all prices are justified by providing an iso-revenue reallocation for the hypothetical removal of any single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature.

econ.TH↗

arXiv2021

Machine Learning-powered Iterative Combinatorial Auctions

We present a machine learning-powered iterative combinatorial auction (MLCA). The main goal of integrating machine learning (ML) into the auction is to improve preference elicitation, which is a major challenge in large combinatorial auctions (CAs). In contrast to prior work, our auction design uses value queries instead of prices to drive the auction. The ML algorithm is used to help the auction decide which value queries to ask in every iteration. While using ML inside a CA introduces new challenges, we demonstrate how we obtain a design that is individually rational, satisfies no-deficit, has good incentives, and is computationally practical. We benchmark our new auction against the well-known combinatorial clock auction (CCA). Our results indicate that, especially in large domains, MLCA can achieve significantly higher allocative efficiency than the CCA, even with only a small number of value queries.

cs.GT↗

arXiv2020

iMLCA: Machine Learning-powered Iterative Combinatorial Auctions with Interval Bidding

Preference elicitation is a major challenge in large combinatorial auctions because the bundle space grows exponentially in the number of items. Recent work has used machine learning (ML) algorithms to identify a small set of bundles to query from each bidder. However, a shortcoming of this prior work is that bidders must submit exact values for the queried bundles, which can be quite costly. To address this, we propose iMLCA, a new ML-powered iterative combinatorial auction with interval bidding (i.e., where bidders submit upper and lower bounds instead of exact values). To steer the auction towards an efficient allocation, we introduce a price-based activity rule, asking bidders to tighten bounds on relevant bundles only. In our experiments, iMLCA achieves the same allocative efficiency as the prior ML-based auction that uses exact bidding. Moreover, it outperforms the well-known combinatorial clock auction in a realistically-sized domain.

cs.GT↗

arXiv2020

Computing Bayes-Nash Equilibria in Combinatorial Auctions with Verification

We present a new algorithm for computing pure-strategy $\varepsilon$-Bayes-Nash equilibria ($\varepsilon$-BNEs) in combinatorial auctions with continuous value and action spaces. An essential innovation of our algorithm is to separate the algorithm's search phase (for finding the $\varepsilon$-BNE) from the verification phase (for computing the $\varepsilon$). Using this approach, we obtain an algorithm that is both very fast and provides theoretical guarantees on the $\varepsilon$ it finds. Our main technical contribution is a verification method which allows us to upper bound the $\varepsilon$ across the whole continuous value space without making assumptions about the mechanism. Using our algorithm, we can now compute $\varepsilon$-BNEs in multi-minded domains that are significantly more complex than what was previously possible to solve. We release our code under an open-source license to enable researchers to perform algorithmic analyses of auctions, to enable bidders to analyze different strategies, and to facilitate many other applications.

cs.GT↗

arXiv2015

Games and Meta-Games: Pricing Rules for Combinatorial Mechanisms

In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This paper offers a new characterization of approximate incentive-compatibility by casting the pricing problem as a meta-game between the center and the participating agents. Through a suitable set of simplifications, we describe the equilibrium of this game as a variational problem. We use this to characterize the space of optimal prices, enabling closed-form solutions in restricted cases, and numerically-determined prices in the general case. We offer theory motivating this approach, and numerical experiments showing its application.

cs.GT↗

arXiv2014

Spectral goodness of fit for network models

We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of an observed network. SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.

cs.SI↗

arXiv2013

Communication Network Design: Balancing Modularity and Mixing via Optimal Graph Spectra

By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for the specific features of social networks, such as the notion of teams. We fill this gap by demonstrating how desirable aspects of organizational structure can be mapped parsimoniously onto the spectrum of the graph Laplacian allowing the specification of structural objectives and build on recent advances in non-convex programming to optimize them. This design framework is general, but we focus here on the problem of creating graphs that balance high modularity and low mixing time, and show how "liaisons" rather than brokers maximize this objective.

cs.SI↗

arXiv2012

Payment Rules through Discriminant-Based Classifiers

In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality.

cs.GT↗

arXiv2012

Quantifying the Strategyproofness of Mechanisms via Metrics on Payoff Distributions

Strategyproof mechanisms provide robust equilibrium with minimal assumptions about knowledge and rationality but can be unachievable in combination with other desirable properties such as budget-balance, stability against deviations by coalitions, and computational tractability. In the search for maximally-strategyproof mechanisms that simultaneously satisfy other desirable properties, we introduce a new metric to quantify the strategyproofness of a mechanism, based on comparing the payoff distribution, given truthful reports, against that of a strategyproof "reference" mechanism that solves a problem relaxation. Focusing on combinatorial exchanges, we demonstrate that the metric is informative about the eventual equilibrium, where simple regretbased metrics are not, and can be used for online selection of an effective mechanism.

cs.GT↗