Abstract
The envy-free pricing problem can be stated as finding a pricing and allocation scheme in which each consumer is allocated a set of items that maximize her utility under the pricing. The goal is to maximize seller revenue. We study the problem with general supply constraints which are given as an independence system defined over the items. The constraints, for example, can be a number of linear constraints or matroids. This captures the situation where items do not pre-exist, but are produced in reflection of consumer valuation of the items under the limit of resources.
This paper focuses on the case of unit-demand consumers. In the setting, there are n consumers and m items; each item may be produced in multiple copies. Each consumer iāāā[n] has a valuation v ij on item j in the set S i in which she is interested. She must be allocated (if any) an item which gives the maximum (non-negative) utility. Suppose we are given an Ī±-approximation oracle for finding the maximum weight independent set for the given independence system (or a slightly stronger oracle); for a large number of natural and interesting supply constraints, constant approximations are available. We obtain the following results.
-
O(Ī±logn)-approximation for the general case.
-
O(Ī±k)-approximation when each consumer is interested in at most k distinct types of items.
-
O(Ī±f)-approximation when each item is interesting to at most f consumers.
Note that the final two results were previously unknown even without the independence system constraint.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balcan, M.-F., Blum, A.: Approximation algorithms and online mechanisms for item pricing. In: EC 2006, pp. 29ā35. ACM, New York (2006)
Briest, P.: Uniform budgets and the envy-free pricing problem. In: ICALP (1), pp. 808ā819 (2008)
Briest, P., Krysta, P.: Single-minded unlimited supply pricing on sparse instances. In: SODA 2006, pp. 1093ā1102 (2006)
Chekuri, C.: Personal Communication (2010)
Chekuri, C., VondrƔk, J., Zenklusen, R.: Multi-budgeted matchings and matroid intersection via dependent rounding (2010) (manuscript)
Chen, N., Ghosh, A., Vassilvitskii, S.: Optimal envy-free pricing with metric substitutability. In: EC 2008, pp. 60ā69 (2008)
Frieze, A.M., Clarke, M.R.B.: Approximation algorithms for the m-dimensional 0-1 knapsack problem: Worst-case and probabilistic analyses. European Journal of Operational ResearchĀ 15(1), 100ā109 (1984)
Goldberg, A.V., Hartline, J.D.: Competitive auctions for multiple digital goods. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol.Ā 2161, pp. 416ā427. Springer, Heidelberg (2001)
Goldberg, A.V., Hartline, J.D., Wright, A.: Competitive auctions and digital goods. In: SODA, pp. 735ā744 (2001)
Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitues. Journal of Economic TheoryĀ 87, 95ā124 (1999)
Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: SODA, pp. 1164ā1173 (2005)
Hartline, J.D., Koltun, V.: Near-optimal pricing in near-linear time. In: Dehne, F., LĆ³pez-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol.Ā 3608, pp. 422ā431. Springer, Heidelberg (2005)
Koopmans, T., Beckmann, M.: Assignment problems and the location of economic activities. EconometricaĀ 25, 53ā76 (1957)
Lee, J., Mirrokni, V.S., Nagarajan, V., Sviridenko, M.: Non-monotone submodular maximization under matroid and knapsack constraints. In: STOC, pp. 323ā332 (2009)
Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency, vol.Ā 24. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Im, S., Lu, P., Wang, Y. (2010). Envy-Free Pricing with General Supply Constraints. In: Saberi, A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17572-5_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-17572-5_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17571-8
Online ISBN: 978-3-642-17572-5
eBook Packages: Computer ScienceComputer Science (R0)