Online Learning in Online Auctions

University of California, Berkeley, Berkeley, California, United States
Theoretical Computer Science (Impact Factor: 0.52). 08/2003; 324(2-3). DOI: 10.1016/j.tcs.2004.05.012
Source: CiteSeer

ABSTRACT We consider the problem of revenue maximization in online auctions, that is, auctions in which bids are received and dealt with one-by-one. In this note, we demonstrate that results from online learning can be usefully applied in this context, and we derive a new auction for digital goods that achieves a constant competitive ratio with respect to the best possible (o#ine) fixed price revenue. This substantially improves upon the best previously known competitive ratio [3] of O(exp( # log log h)) for this problem. We apply our techniques to the related problem of online posted price mechanisms, where the auctioneer declares a price and a bidder only communicates his acceptance/rejection of the price. For this problem we obtain results that are (somewhat surprisingly) similar to the online auction problem.

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    ABSTRACT: We consider pricing in settings where a consumer discovers his value for a good only as he uses it, and the value evolves with each use. We explore simple and natural pricing strategies for a seller in this setting, under the assumption that the seller knows the distribution from which the consumer's initial value is drawn, as well as the stochastic process that governs the evolution of the value with each use. We consider the differences between up-front or "buy-it-now" pricing (BIN), and "pay-per-play" (PPP) pricing, where the consumer is charged per use. Our results show that PPP pricing can be a very effective mechanism for price discrimination, and thereby can increase seller revenue. But it can also be advantageous to the buyers, as a way of mitigating risk. Indeed, this mitigation of risk can yield a larger pool of buyers. We also show that the practice of offering free trials is largely beneficial. We consider two different stochastic processes for how the buyer's value evolves: In the first, the key random variable is how long the consumer remains interested in the product. In the second process, the consumer's value evolves according to a random walk or Brownian motion with reflection at 1, and absorption at 0.
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    ABSTRACT: Multi-attribute resource allocation problems involve the allocation of resources on the basis of several attributes, therefore, the definition of a fairness method for this kind of auctions should be formulated from a multi-dimensional perspective. Under such point of view, fairness should take into account all the attributes involved in the allocation problem, since focusing on just a single attribute may compromise the allocations regarding the remainder attributes (e.g. incurring in delayed or bad quality tasks). In this paper, we present a multi-dimensional fairness approach based on priorities. For that purpose, a recurrent auction scenario is assumed, in which the auctioneer keeps track of winner and losers. From that information, the priority methods are defined based on the lost auctions number, the number of consecutive loses, and the fitness of their loser bids. Moreover, some methods contain a probabilistic parameter that enables handling wealth ranking disorders due to fairness. We test our approach in real-data based simulator which emulates an industrial production environment where several resource providers compete to perform different tasks. The results pointed that multi-dimensional fairness incentives agents to remain in the market whilst it improves the equity of the wealth distribution without compromising the quality of the allocation attributes.
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    ABSTRACT: We propose a uniform approach for the design and analysis of prior-free competitive auctions and online auctions. Our philosophy is to view the benchmark function as a variable parameter of the model and study a broad class of functions instead of a individual target benchmark. We consider a multitude of well-studied auction settings, and improve upon a few previous results. (1) Multi-unit auctions. Given a $\beta$-competitive unlimited supply auction, the best previously known multi-unit auction is $2\beta$-competitive. We design a $(1+\beta)$-competitive auction reducing the ratio from $4.84$ to $3.24$. These results carry over to matroid and position auctions. (2) General downward-closed environments. We design a $6.5$-competitive auction improving upon the ratio of $7.5$. Our auction is noticeably simpler than the previous best one. (3) Unlimited supply online auctions. Our analysis yields an auction with a competitive ratio of $4.12$, which significantly narrows the margin of $[4,4.84]$ previously known for this problem. A particularly important tool in our analysis is a simple decomposition lemma, which allows us to bound the competitive ratio against a sum of benchmark functions. We use this lemma in a "divide and conquer" fashion by dividing the target benchmark into the sum of simpler functions.


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