757 research outputs found

    On Revenue Monotonicity in Combinatorial Auctions

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    Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for mm items and nn buyers in the Bayesian setting, specified by a valuation function vv and a set FF of nmnm independent item-type distributions. Let REV(v,F)REV(v, F) denote the maximum revenue achievable under FF by any incentive compatible mechanism. Intuitively, one would expect that REV(v,G)REV(v,F)REV(v, G)\geq REV(v, F) if distribution GG stochastically dominates FF. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when vv is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions vv, showing that REV(v,G)cREV(v,F)REV(v, G)\geq c\,REV(v, F) if GG stochastically dominates FF under vv where c>0c>0 is a universal constant. Previously, approximate monotonicity was known only for the case n=1n=1: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.Comment: 10 page

    Randomized Revenue Monotone Mechanisms for Online Advertising

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    Online advertising is the main source of revenue for many Internet firms. A central component of online advertising is the underlying mechanism that selects and prices the winning ads for a given ad slot. In this paper we study designing a mechanism for the Combinatorial Auction with Identical Items (CAII) in which we are interested in selling kk identical items to a group of bidders each demanding a certain number of items between 11 and kk. CAII generalizes important online advertising scenarios such as image-text and video-pod auctions [GK14]. In image-text auction we want to fill an advertising slot on a publisher's web page with either kk text-ads or a single image-ad and in video-pod auction we want to fill an advertising break of kk seconds with video-ads of possibly different durations. Our goal is to design truthful mechanisms that satisfy Revenue Monotonicity (RM). RM is a natural constraint which states that the revenue of a mechanism should not decrease if the number of participants increases or if a participant increases her bid. [GK14] showed that no deterministic RM mechanism can attain PoRM of less than ln(k)\ln(k) for CAII, i.e., no deterministic mechanism can attain more than 1ln(k)\frac{1}{\ln(k)} fraction of the maximum social welfare. [GK14] also design a mechanism with PoRM of O(ln2(k))O(\ln^2(k)) for CAII. In this paper, we seek to overcome the impossibility result of [GK14] for deterministic mechanisms by using the power of randomization. We show that by using randomization, one can attain a constant PoRM. In particular, we design a randomized RM mechanism with PoRM of 33 for CAII

    Envy Freedom and Prior-free Mechanism Design

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    We consider the provision of an abstract service to single-dimensional agents. Our model includes position auctions, single-minded combinatorial auctions, and constrained matching markets. When the agents' values are drawn from a distribution, the Bayesian optimal mechanism is given by Myerson (1981) as a virtual-surplus optimizer. We develop a framework for prior-free mechanism design and analysis. A good mechanism in our framework approximates the optimal mechanism for the distribution if there is a distribution; moreover, when there is no distribution this mechanism still performs well. We define and characterize optimal envy-free outcomes in symmetric single-dimensional environments. Our characterization mirrors Myerson's theory. Furthermore, unlike in mechanism design where there is no point-wise optimal mechanism, there is always a point-wise optimal envy-free outcome. Envy-free outcomes and incentive-compatible mechanisms are similar in structure and performance. We therefore use the optimal envy-free revenue as a benchmark for measuring the performance of a prior-free mechanism. A good mechanism is one that approximates the envy free benchmark on any profile of agent values. We show that good mechanisms exist, and in particular, a natural generalization of the random sampling auction of Goldberg et al. (2001) is a constant approximation
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