Article

Online Learning in Online Auctions

Theoretical Computer Science (Impact Factor: 0.52). 08/2003; 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.

0 Bookmarks
 · 
124 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: We study a multi-round optimization setting in which in each round a player may select one of several actions, and each action produces an outcome vector, not observable to the player until the round ends. The final payoff for the player is computed by applying some known function f to the sum of all outcome vectors (e.g., the minimum of all coordinates of the sum). We show that standard notions of performance measure (such as comparison to the best single action) used in related expert and bandit settings (in which the payoff in each round is scalar) are not useful in our vector setting. Instead, we propose a different performance measure, and design algorithms that have vanishing regret with respect to our new measure.
    Proceedings of the 5th conference on Innovations in theoretical computer science; 01/2014
  • Source
    [Show abstract] [Hide abstract]
    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.
    11/2014;
  • Source
    [Show abstract] [Hide abstract]
    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.
    11/2014;

Full-text

Download
0 Downloads
Available from