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Online Auctions with Re-usable Goods
This paper concerns the design of mechanisms for online scheduling in which agents bid for access to a re-usable resource such as processor time or wireless network access. Each agent is assumed to arrive and depart dynamically, and in the basic model require the resource for one unit of time. We seek mechanisms that are truthful in the sense that truthful revelation of arrival, departure and value information is a dominant strategy, and that are online in the sense that they make allocation decisions without knowledge of the future. First, we provide two characterizations for the class of truthful online allocation rules. The characterizations extend beyond the typical single-parameter settings, and formalize the role of restricted misreporting in reversing existing price-based characterizations. Second, we present an online auction for unit-length jobs that achieves total value that is 2-competitive with the maximum offline value. We prove that no truthful deterministic online mechanism can achieve a better competitive ratio. Third, we consider revenue competitiveness and prove that no deterministic truthful online auction has revenue that is constant-competitive with that of the offline Vickrey-Clarke-Groves (VCG) mechanism We provide a randomized online auction that achieves a competitive ratio of O(log h), where h is the ratio of maximum value to minimum value among the agents; this mechanism does not require prior knowledge of h. Finally, we generalize our model to settings with multiple re-usable goods and to agents with different job lengths.Engineering and Applied Science
The power of verification for one-parameter agents
We initiate the study of mechanisms with verification for one-parameter agents. We give an algorithmic characterization of such mechanisms and show that they are provably better than mechanisms without verification, i.e., those previously considered in the literature. These results are obtained for a number of optimization problems motivated by the Internet and recently studied in the algorithmic mechanism design literature. The characterization can be regarded as an alternative approach to existing techniques to design truthful mechanisms. The construction of such mechanisms reduces to the construction of an algorithm satisfying certain âmonotonicityâ conditions which, for the case of verification, are much less stringent. In other words, verification makes the construction easier and the algorithm more efficient (both computationally and in terms of approximability)
New Constructions for Mechanisms with Verification
A social choice function A is implementable with verification
if there exists a payment scheme P such that (A,P) is a truthful mechanism for verifiable agents [Nisan and Ronen, STOC 99]. We give a simple sufficient condition for a social choice function to be implementable with verification for comparable types. Comparable types are a generalization of the well-studied one-parameter agents. Based on this
characterization, we show that a large class of objective functions Ό admit social choice functions that are implementable with verification and minimize (or maximize) Ό.We then focus on the well-studied case of oneparameter
agents.We give a general technique for constructing efficiently
computable social choice functions that minimize or approximately minimize objective functions that are non-increasing and neutral (these are functions that do not depend on the valuations of agents that have no
work assigned to them). As a corollary we obtain efficient online and offline mechanisms with verification for some hard scheduling problems on related machines
Single Parameter Combinatorial Auctions with Partially Public Valuations
We consider the problem of designing truthful auctions, when the bidders'
valuations have a public and a private component. In particular, we consider
combinatorial auctions where the valuation of an agent for a set of
items can be expressed as , where is a private single parameter
of the agent, and the function is publicly known. Our motivation behind
studying this problem is two-fold: (a) Such valuation functions arise naturally
in the case of ad-slots in broadcast media such as Television and Radio. For an
ad shown in a set of ad-slots, is, say, the number of {\em unique}
viewers reached by the ad, and is the valuation per-unique-viewer. (b)
From a theoretical point of view, this factorization of the valuation function
simplifies the bidding language, and renders the combinatorial auction more
amenable to better approximation factors. We present a general technique, based
on maximal-in-range mechanisms, that converts any -approximation
non-truthful algorithm () for this problem into
and -approximate truthful
mechanisms which run in polynomial time and quasi-polynomial time,
respectively
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