Results 11  20
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92
Buying Cheap is Expensive: Hardness of NonParametric MultiProduct Pricing
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 68
, 2006
"... We investigate nonparametric unitdemand pricing problems, in which the goal is to find revenue maximizing prices for products P based on a set of consumer profiles C obtained, e.g., from an eCommerce website. A consumer profile consists of a number of nonzero budgets and a ranking of all the pro ..."
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Cited by 22 (6 self)
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We investigate nonparametric unitdemand pricing problems, in which the goal is to find revenue maximizing prices for products P based on a set of consumer profiles C obtained, e.g., from an eCommerce website. A consumer profile consists of a number of nonzero budgets and a ranking of all the products the consumer is interested in. Once prices are fixed, each consumer chooses to buy one of the products she can afford based on some predefined selection rule. We distinguish between the minbuying, maxbuying, and rankbuying models. For the minbuying and general rankbuying models the best known approximation ratio is O(log C) and, previously, the problem was only known to be APXhard. We obtain the first (near) tight lower bound showing that the problem is not approximable within O(log ε C) for some ε> 0, unless NP ⊆ DTIME(n loglog n). Going to slightly stronger (still reasonable) complexity theoretic assumptions we prove inapproximability within O(ℓ ε) (ℓ being an upper bound on the number of nonzero budgets per consumer) and O(P  ε) and provide matching upper bounds. Surprisingly, these hardness results hold even if a price ladder constraint, i.e., a predefined total order on the prices of all products, is given. This changes if we require that in the rankbuying model consumers’ budgets are consistent with their
Bayesian Incentive Compatibility via Matchings
"... We give a simple reduction from Bayesian incentive compatible mechanism design to algorithm design in settings where the agents ’ private types are multidimensional. The reduction preserves performance up to an additive loss that can be made arbitrarily small in polynomial time in the number of agen ..."
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Cited by 21 (1 self)
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We give a simple reduction from Bayesian incentive compatible mechanism design to algorithm design in settings where the agents ’ private types are multidimensional. The reduction preserves performance up to an additive loss that can be made arbitrarily small in polynomial time in the number of agents and the size of the agents ’ type spaces. 1
Mechanism design for fractional scheduling on unrelated machines
 Automata, Languages and Programming
, 2007
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On the Computational Power of Iterative Auctions I: Demand Queries
 In Proceedings of the 6th ACM Conference on Electronic Commerce (EC
, 2005
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On the Computational Power of Demand Queries
"... We study the computational power of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their “demand” under these prices. We prove several results regarding such auctions that u ..."
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Cited by 16 (3 self)
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We study the computational power of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their “demand” under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries cannot do so; (3) that such auctions that only use item prices may solve allocation problems in communication cost that is exponentially lower than the cost incurred by auctions that use prices for bundles. For the latter result, we initiate the study of how prices of bundles can be represented when they are not linear, and show that the “default” representation has severe limitations. Our results hold for any series of demand queries with polynomial length, without any additional restrictions on the queries (e.g., to ascending prices).
Efficient and Strategyproof Spectrum Allocations in Multichannel Wireless Networks
"... Abstract—In this paper, we study the spectrum assignment problem for wireless access networks. We assume that each secondary user will bid a certain value for exclusive usage of some spectrum channels for a certain time period or for a certain time duration. A secondary user may also require the exc ..."
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Cited by 15 (4 self)
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Abstract—In this paper, we study the spectrum assignment problem for wireless access networks. We assume that each secondary user will bid a certain value for exclusive usage of some spectrum channels for a certain time period or for a certain time duration. A secondary user may also require the exclusive usage of a subset of channels, or require the exclusive usage of a certain number of channels. Thus, several versions of problems are formulated under various different assumptions. For the majority of problems, we design PTAS or efficient constantapproximation algorithms such that overall profit is maximized. Here, the profit is defined as the total bids of all satisfied secondary users. As a side product of our algorithms, we are able to show that a previously studied Scheduling Split Interval Problem (SSIP) [2], in which each job is composed of t intervals, cannot be approximated within Oðt1 Þ for any small>0 unless NP ZPP. Opportunistic spectrum usage, although a promising technology, could suffer from the selfish behavior of secondary users. In order to improve opportunistic spectrum usage, we then propose to combine the game theory with wireless modeling. We show how to design a truthful mechanism based on all of these algorithms such that the best strategy of each secondary user to maximize its own profit is to truthfully report its actual bid.
Secondary spectrum auctions for symmetric and submodular bidders
 In Proc. 13th Conf. Electronic Commerce (EC
, 2012
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Reducing revenue to welfare maximization: Approximation algorithms and other generalizations
 IN SODA
, 2013
"... It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multidimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly comb ..."
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It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multidimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly combinatorial) demand constraints. This reduction provides a polytime solution to the optimal mechanism design problem in all auction settings where welfare optimization can be solved efficiently, but it is fragile to approximation and cannot provide solutions to settings where welfare maximization can only be tractably approximated. In this paper, we extend the reduction to accommodate approximation algorithms, providing an approximation preserving reduction from (truthful) revenue maximization to (not necessarily truthful) welfare maximization. The mechanisms output by our reduction choose allocations via blackbox calls to welfare approximation on randomly selected inputs, thereby generalizing also our earlier structural results on optimal multidimensional mechanisms to approximately optimal mechanisms. Unlike [12], our results here are obtained through novel uses of the Ellipsoid algorithm and other optimization techniques over nonconvex regions.
A characterization of 2player mechanisms for scheduling
, 2008
"... We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechan ..."
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Cited by 13 (5 self)
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We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechanism partitions the tasks into groups so that the tasks in each group are allocated independently of the other groups. Tasks in a group of size at least two are allocated by an affine minimizer and tasks in singleton groups by a taskindependent mechanism. This characterization is about all truthful mechanisms, including those with unbounded approximation ratio. A direct consequence of this approach is that the approximation ratio of mechanisms for two players is 2, even for two tasks. In fact, it follows that for two players, VCG is the unique algorithm with optimal approximation 2. This characterization provides some support that any decisive truthful mechanism (for 3 or more players) partitions the tasks into groups some of which are allocated by affine minimizers, while the rest are allocated by a threshold mechanism (in which a task is allocated to a player when it is below a threshold value which depends only on the values of the other players). We also show here that the class of threshold mechanisms is identical to the class of additive mechanisms.
A lower bound of 1+φ for truthful scheduling mechanisms
 In The Proc. of the 32nd International Symposium on Mathematical Foundations of Computer Science (MFCS
"... Abstract. We give an improved lower bound for the approximation ratio of truthful mechanisms for the unrelated machines scheduling problem. The mechanism design version of the problem which was proposed and studied in a seminal paper of Nisan and Ronen is at the core of the emerging area of Algorith ..."
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Abstract. We give an improved lower bound for the approximation ratio of truthful mechanisms for the unrelated machines scheduling problem. The mechanism design version of the problem which was proposed and studied in a seminal paper of Nisan and Ronen is at the core of the emerging area of Algorithmic Game Theory. The new lower bound 1 + φ ≈ 2.618 is a step towards the final resolution of this important problem. 1