Abstract
Given a seller with m amount of items, a sequence of users {u 1, u 2, ...} come one by one, the seller must set the unit price and assign some amount of items to each user on his/her arrival. Items can be sold fractionally. Each u i has his/her value function v i (·) such that v i (x) is the highest unit price u i is willing to pay for x items. The objective is to maximize the revenue by setting the price and amount of items for each user. In this paper, we have the following contributions: if the highest value h among all v i (x) is known in advance, we first show the lower bound of the competitive ratio is O(logh), then give an online algorithm with competitive ratio O(logh); if h is not known in advance, we give an online algorithm with competitive ratio \(O(h^{3\log^{-1/2}h})\).
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References
Balcan, M.-F., Blum, A.: Approximation Algorithms and Online Mechanisms for Item Pricing. Thoery of Computing 3, 179–195 (2007)
Cheung, M., Swamy, C.: Approximation Algorithms for Single-minded Envy-free Profit-maximization Problems with Limited Supply. In: Proc. of 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2008), pp. 35–44 (2008)
Balcan, N., Blum, A., Mansour, Y.: Item pricing for revenue maximization. In: Proc. of the 9th ACM Conference on Electronic Commerce (EC 2008), pp. 50–59 (2008)
Bansal, N., Chen, N., Cherniavsky, N., Rurda, A., Schieber, B., Sviridenko, M.: Dynamic pricing for impatient bidders. ACM Transactions on Algorithms 6(2) (March 2010)
Chen, N., Deng, X.: Envy-Free Pricing in Multi-item Markets. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 418–429. Springer, Heidelberg (2010)
Chen, N., Ghosh, A., Vassilvitskii, S.: Optimal envy-free pricing with metric substitutability. In: Proc. of the 9th ACM Conference on Electronic Commerce (EC 2008), pp. 60–69 (2008)
Elbassioni, K., Sitters, R., Zhang, Y.: A quasi-PTAS for profit-maximizing pricing on line graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 451–462. Springer, Heidelberg (2007)
Fiat, A., Wingarten, A.: Envy, Multi Envy, and Revenue Maximization. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 498–504. Springer, Heidelberg (2009)
Grigoriev, A., van Loon, J., Sitters, R., Uetz, M.: How to Sell a Graph: Guidelines for Graph Retailers. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 125–136. Springer, Heidelberg (2006)
Guruswami, V., Hartline, J., Karlin, A., Kempe, D., Kenyon, C., McSherry, F.: On Profit-Maximizing Envy-Free Pricing. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), pp. 1164–1173 (2005)
Im, S., Lu, P., Wang, Y.: Envy-Free Pricing with General Supply Constraints. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 483–491. Springer, Heidelberg (2010)
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Zhang, Y., Chin, F.Y.L., Ting, HF. (2011). Competitive Algorithms for Online Pricing. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_35
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DOI: https://doi.org/10.1007/978-3-642-22685-4_35
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