Learning to bid in revenue-maximizing auctions

We consider the problem of the optimization of bidding strategies in prior-dependent revenue-maximizing auctions, when the seller fixes the reserve prices based on the bid distributions. Our study is done in the setting where one bidder is strategic. Using a variational approach, we study the complexity of the original objective and we introduce a relaxation of the objective functional in order to use gradient descent methods. Our approach is simple, general and can be applied to various value distributions and revenue-maximizing mechanisms. The new strategies we derive yield massive uplifts compared to the traditional truthfully bidding strategy

Mechanism Design via Correlation Gap

For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al.\ (SODA10) quantifies how much we {}"lose" in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al.\ for several environments. In particular, we show that it gives an $e/(e-1)$-approximation for matroid environments, gives asymptotically a $1/(1-1/\sqrt{2\pi k})$-approximation for the important sub-case of $k$-unit auctions, and gives a $(p+1)$-approximation for environments with $p$-independent set system constraints

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players' types are drawn from an underlying distribution and may be correlated, and the goal is to minimize the expected total payment made by the mechanism. We formulate a notion of incentive compatibility (IC) that we call {\em support-based IC} that is substantially more robust than Bayesian IC, and develop black-box reductions from support-based-IC mechanism design to algorithm design. For single-dimensional settings, this black-box reduction applies even when we only have an LP-relative {\em approximation algorithm} for the algorithmic problem. Thus, we obtain near-optimal mechanisms for various covering settings including single-dimensional covering problems, multi-item procurement auctions, and multidimensional facility location.Comment: Major changes compared to the previous version. Please consult this versio

Truth and Regret in Online Scheduling

We consider a scheduling problem where a cloud service provider has multiple units of a resource available over time. Selfish clients submit jobs, each with an arrival time, deadline, length, and value. The service provider's goal is to implement a truthful online mechanism for scheduling jobs so as to maximize the social welfare of the schedule. Recent work shows that under a stochastic assumption on job arrivals, there is a single-parameter family of mechanisms that achieves near-optimal social welfare. We show that given any such family of near-optimal online mechanisms, there exists an online mechanism that in the worst case performs nearly as well as the best of the given mechanisms. Our mechanism is truthful whenever the mechanisms in the given family are truthful and prompt, and achieves optimal (within constant factors) regret. We model the problem of competing against a family of online scheduling mechanisms as one of learning from expert advice. A primary challenge is that any scheduling decisions we make affect not only the payoff at the current step, but also the resource availability and payoffs in future steps. Furthermore, switching from one algorithm (a.k.a. expert) to another in an online fashion is challenging both because it requires synchronization with the state of the latter algorithm as well as because it affects the incentive structure of the algorithms. We further show how to adapt our algorithm to a non-clairvoyant setting where job lengths are unknown until jobs are run to completion. Once again, in this setting, we obtain truthfulness along with asymptotically optimal regret (within poly-logarithmic factors)

Bidding Behavior in Multi-Unit Auctions - An Experimental Investigation and some Theoretical Insights

We present laboratory experiments of five different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with at demand for two units. We test whether expected demand reduction occurs in open and sealed-bid uniform-price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed-bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units. We also provide some theoretical insights concerning the equilibria of uniform-price auctions with incomplete information.Multi-Unit Auctions; Demand Reduction; Experimental Economics

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

The value of relationships : evidence from a supply shock to Kenyan rose exports

This paper provides evidence on the importance of reputation, intended as beliefs buyers hold about seller's reliability, in the context of the Kenyan rose export sector. A model of reputation and relational contracting is developed and tested. We show that 1) the value of the relationship increases with the age of the relationship; 2) during an exogenous negative supply shock sellers prioritize relationships consistently with the predictions of the model; and 3) reliability at the time of the shock positively correlates with future survival and relationship value. Models exclusively focussing on enforcement or insurance considerations cannot account for the evidence

BIDDING BEHAVIOR IN MULTI-UNIT AUCTIONS - AN EXPERIMENTAL INVESTIGATION AND SOME THEORETICAL INSIGHTS

We present laboratory experiments of five different multi-unit auction mechanisms. Two units of a homogeneous object were auctioned off among two bidders with flat demand for two units. We test whether expected demand reduction occurs in open and sealed-bid uniform-price auctions. Revenue equivalence is tested for these auctions as well as for the Ausubel, the Vickrey and the discriminatory sealed-bid auction. Furthermore, we compare the five mechanisms with respect to the efficient allocation of the units. We also provide some theoretical insights concerning the equilibria of uniform-price auctions with incomplete information.Multi–Unit Auctions, Demand Reduction, Experimental Economics.

Trust and Experience in Online Auctions

This paper aims to shed light on the complexities and difficulties in predicting the effects of trust and the experience of online auction participants on bid levels in online auctions. To provide some insights into learning by bidders, a field study was conducted first to examine auction and bidder characteristics from eBay auctions of rare coins. We proposed that such learning is partly because of institutional-based trust. Data were then gathered from 453 participants in an online experiment and survey, and a structural equation model was used to analyze the results. This paper reveals that experience has a nonmonotonic effect on the levels of online auction bids. Contrary to previous research on traditional auctions, as online auction bidders gain more experience, their level of institutional-based trust increases and leads to higher bid levels. Data also show that both a bidder’s selling and bidding experiences increase bid levels, with the selling experience having a somewhat stronger effect. This paper offers an in-depth study that examines the effects of experience and learning and bid levels in online auctions. We postulate this learning is because of institutional-based trust. Although personal trust in sellers has received a significant amount of research attention, this paper addresses an important gap in the literature by focusing on institutional-based trust