Optimal pricing of capacitated networks

Grigoriev, Alexander; Loon, Joyce van; Sitters, René; Uetz, Marc

doi:10.1002/net.20260

Cited by 9 publications

(13 citation statements)

References 21 publications

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“…, K , we can use price vectors maximizing the revenue in the S k -restricted problems, with given set of winners W = S k . Notice that, for any set of winners W ⊆ J , the price vector maximizing the revenue obtained from W can be found in polynomial time by solving a simple linear program; see (Grigoriev et al 2009;Guruswami et al 2005). Unfortunately, this approach does not necessarily lead to any provable improvement of the performance guarantee.…”

Section: Improved Analysis and Asymptotic Tightnessmentioning

confidence: 99%

On the complexity of a bundle pricing problem

2011

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Section: Improved Analysis and Asymptotic Tightnessmentioning

confidence: 99%

On the complexity of a bundle pricing problem

2011

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“…Guruswami et al [8] propose a polynomial time dynamic programming algorithm when the valuations are bounded by a constant, and a pseudo-polynomial time dynamic programming algorithm when the lengths of the sub-paths are bounded by a constant. Note that the problem can be interpreted as a bilevel linear program, and if either the price vector or the set of winners is known, the problem is polynomially solvable [6,8], even under the requirement of integral prices. Balcan and Blum [1] derive an O(log m)-approximation algorithm for the highway problem, improving upon the previous O(log m + log n)-approximation of Guruswami et al [8], where m is the number of highway segments and n is the number of customers.…”

Section: Related Workmentioning

confidence: 99%

On the Complexity of the Highway Pricing Problem

Grigoriev

Loon

Uetz

2010

SOFSEM 2010: Theory and Practice of Computer Science

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On the Complexity of the Highway Pricing Problem RM/08/030 JEL code: C44, C61 Abstract. The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is (weakly) NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so far it has resisted any attempt for constant-factor approximation algorithms. We relate the tractability of the problem to structural properties of customers' valuations. We show that the problem becomes NP-hard as soon as the average valuations of customers are not homogeneous, even under further restrictions such as monotonicity. Moreover, we derive an efficient approximation algorithm, parameterized along the inhomogeneity of customers' valuations. Finally, we discuss extensions of our results that go beyond the highway pricing problem.

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“…For limited supply when the number of available copies per item is bounded by C, Grigoriev et al [11] propose a dynamic programming algorithm that computes the optimal solution in time O(n 2C B 2C m), where n is the number of agents, m the number of items, and B an upper bound on the valuations. For C constant, and by appropriately discretizing B, this algorithm can be used to derive an FPTAS for this version of the highway problem.…”

Section: The Highway Problemmentioning

confidence: 99%

Envy, Multi Envy, and Revenue Maximization

Fiat

Wingarten

2009

Lecture Notes in Computer Science

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We study the envy free pricing problem faced by a seller IntroductionWe consider the combinatorial auction setting where there are several different items for sale, not all items are identical, and agents have valuations for subsets of items. We allow the seller to have identical copies of an item. We distinguish between the case of limited supply (e.g., physical goods) and that of unlimited supply (e.g., digital goods). Agents have known valuations for subsets of items. We assume free disposal, i.e., the valuation of a superset is ≥ the valuation of a subset. Let S be a set of items, agent i has valuation v i (S) for set S. The valuation functions, v i , are public knowledge. Ergo, we are not concerned with issues of truthfulness or incentive compatible bidding. Our concern here is to maximize revenue in an envy free manner.Our goal is to determine prices for sets of items while (approximately) maximizing revenue. The output of the mechanism is a payment function p that assigns prices to sets of items and an allocation a. Although there are exponentially many such sets, we will only consider payments functions that have a concise representation. For a set of items S let p(S) be the payment required for set S. Let a i be the set assigned to agent i.In general, every agent i has valuation function v i defined over every subset of items.Given a payment function p, and a set of valuation functions v i , let z i = max S (v i (S) − p(S)), and let S i to be a collection of sets such that S ∈ S i if and only if v i (S) − p(S) = z i .We now distinguish between two notions of envy freeness.Definition 1 We say that (a, p) are envy free ifDefinition 2 If a i = ∅ then we say that agent i loses, otherwise we say that agent i wins.Definition 3 A pricing p is monotone if for each subset S and for each collection of subsets C such that S ⊆ T ∈C

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Optimal pricing of capacitated networks

Cited by 9 publications

References 21 publications

On the complexity of a bundle pricing problem

On the complexity of a bundle pricing problem

On the Complexity of the Highway Pricing Problem

Envy, Multi Envy, and Revenue Maximization

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