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Incentive-Compatible Online Auctions for Digital Goods

11/2001;
Source: CiteSeer

ABSTRACT Goldberg et al. [6] recently began the study of incentivecompatible auctions for digital goods, that is, goods which are available in unlimited supply. Many digital goods, however, such as books, music, and software, are sold continuously, rather than in a single round, as is the case for traditional auctions. Hence, it is important to consider what happens in the online version of such auctions. We de ne a model for online auctions for digital goods, and within this model, we examine auctions in which bidders have an incentive to bid their true valuations, that is, incentivecompatible auctions. Since the best oine auctions achieve revenue comparable to the revenue of the optimal xed pricing scheme, we use the latter as our benchmark. We show that deterministic auctions perform poorly relative to this benchmark, but we give a randomized auction which is within a factor O(exp( p log log h)) of the benchmark, where h is the ratio between the highest and lowest bids. As part of this result, we also give a new oine auction, which improves upon the previously best auction in a certain class of auctions for digital goods. We also give lower bounds for both randomized and deterministic online auctions for digital goods. 1

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    • "While in this model the agent's value is private, her arrival time is public. A wide variety of additional online auction settings, such as digital goods [6] [4] and combinatorial auctions [2], have been studied under the assumption of private values and public arrival times. Similarly to our model and the model presented in [20], online settings in which agents arrive in a random order were also considered in [3] [23] [22]. "
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    • "the reflection principle: the random walk with reflection at 1 and absorption at 0 is equivalent to a random walk between [0] [2] with absorption at both 0 and 2. Thus, reaching u in the old walk is equivalent to reaching one of u and its reflection 2 − u in the new walk. Equation (5) is Exercise 17.1 in [14] (proved by considering a martingale related to V t , namely M t = Y 3 t − 3tY t , where Y t = "
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    • "Kleinberg and Leighton study a posted price repeated auction with goods sold sequentially to T bidders who either all have the same fixed private value, private values drawn from a fixed distribution, or private values that are chosen by an oblivious adversary (an adversary that acts independently of observed seller behavior) [15] (see also [7] [8] [14]). Cesa-Bianchi et al. study a related problem of setting the reserve price in a second price auction with multiple (but not repeated) bidders at each round [9]. "
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