Abstract
One-way trading is a fundamental problem in the online algorithms. A seller has some product to be sold to a sequence of buyers \(\{u_1, u_2, \dots \}\) in an online fashion and each buyer \(u_i\) is associated with his accepted unit price \(p_i\), which is known to the seller on the arrival of \(u_i\). The seller needs to decide the amount of products to be sold to \(u_i\) at the then-prevailing price \(p_i\). The objective is to maximize the total revenue of the seller. In this paper, we study the unbounded one-way trading, i.e., the highest unit price among all buyers is unbounded. We also assume that the highest prices of buyers follow some distribution with monotone hazard rate, which is well-adopted in Economics. We investigate two variants, (1) the distribution is on the highest price among all buyers, and (2) a general variant that the prices of buyers is independent and identically distributed. To measure the performance of the algorithms, the expected competitive ratios, \(\mathrm {E}[OPT]/\mathrm {E}[ALG]\) and \(\mathrm {E}[OPT/ALG]\), are considered and constant-competitive algorithms are given if the distributions satisfy the monotone hazard rate.
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References
Babaioff, M., Dughmi, S., Kleinberg, R., Slivkins, A.: Dynamic pricing with limited supply. In: Proceedings of the 13th ACM Conference on Electronic Commerce (EC 2012), pp. 74–91 (2012)
Badanidiyuru, A., Kleinberg, R., Singer, Y.: Learning on a budget: posted price mechanisms for online procurement. In: Proceedings of the 13th ACM Conference on Electronic Commerce (EC 2012), pp. 128–145 (2012)
Balcan, M.-F., Blum, A., Mansour, Y.: Item pricing for revenue maximization. In: Proceedings of the 9th ACM Conference on Electronic Commerce (EC 2008), pp. 50–59 (2008)
Blum, A., Hartline, J.D.: Near-optimal online auctions. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), pp. 1156–1163 (2005)
Blum, A., Gupta, A., Mansour, Y., Sharma, A.: Welfare and profit maximization with production costs. In: Proceedings of 52th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2011), pp. 77–86 (2011)
Chakraborty, T., Even-Dar, E., Guha, S., Mansour, Y., Muthukrishnan, S.: Approximation schemes for sequential posted pricing in multi-unit auctions. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 158–169. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17572-5_13
Chakraborty, T., Huang, Z., Khanna, S.: Dynamic and non-uniform pricing strategies for revenue maximization. In: Proceedings of 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), pp. 495–504 (2009)
Chawla, S., Hartline, J.D., Kleinberg, R.: Algorithmic pricing via virtual valuations. In: Proceedings of the 8th ACM Conference on Electronic Commerce (EC 2007), pp. 243–251 (2007)
Chen, G.-H., Kao, M.-Y., Lyuu, Y.-D., Wong, H.-K.: Optimal buy-and-hold strategies for financial markets with bounded daily returns. SIAM J. Compt. 31(2), 447–459 (2001)
Chin, F.Y.L., Fu, B., Guo, J., Han, S., Hu, J., Jiang, M., Lin, G., Ting, H.-F., Zhang, L., Zhang, Y., Zhou, D.: Competitive algorithms for unbounded one-way trading. Theor. Comput. Sci. 607(1), 35–48 (2015)
Dhangwatnotai, P., Roughgarden, T., Yan, Q.: Revenue maximization with a single sample. Games Econ. Behav. 91, 318–333 (2015)
El-Yaniv, R., Fiat, A., Karp, R.M., Turpin, G.: Competitive analysis of financial games. In: Proceedings of 33th Annual IEEE Symposium on Foundations of Computer Science (FOCS 1992), pp. 372–333 (1992)
El-Yaniv, R., Fiat, A., Karp, R.M., Turpin, G.: Optimal search and one-way trading online algorithms. Algorithmica 30(1), 101–139 (2001)
Fujiwara, H., Iwama, K., Sekiguchi, Y.: Average-case competitive analyses for one-way trading. J. Comb. Optim. 21(1), 83–107 (2011)
Koutsoupias, E., Pierrakos, G.: On the competitive ratio of online sampling auctions. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 327–338. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17572-5_27
Lorenz, J., Panagiotou, K., Steger, A.: Optimal algorithms for k-search with application in option pricing. Algorithmica 55(2), 311–328 (2009)
Mahdian, M., McAfee, R.P., Pennock, D.: The secretary problem with a hazard rate condition. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 708–715. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-92185-1_76
Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)
Zhang, Y., Chin, F.Y.L., Ting, H.-F.: Competitive algorithms for online pricing. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 391–401. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22685-4_35
Zhang, Y., Chin, F.Y.L., Ting, H.-F.: Online pricing for bundles of multiple items. J. Glob. Optim. 58(2), 377–387 (2014)
Acknowledgements
This research is supported by National Key Research and Development Program of China under Grant 2016YFB0201401, China’s NSFC grants (No. 61433012, U1435215, 61402461, 61772489), Hong Kong GRF grant (17210017, HKU 7114/13E), and Shenzhen basic research grant JCYJ20160229195940462.
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Chin, F.Y.L., Lau, F.C.M., Tan, H., Ting, HF., Zhang, Y. (2017). Unbounded One-Way Trading on Distributions with Monotone Hazard Rate. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_36
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