Abstract
We consider the market mechanism to sell two types of products, A and B, to a set of buyers \(I=\{1, 2, ..., n\}\). The amounts of products are \(m_A\) and \(m_B\) respectively. Each buyer i has his information including the budget, the preference and the utility function. On collecting the information from all buyers, the market maker determines the price of each product and allocates some amount of product to each buyer. The objective of the market maker is design a mechanism to achieve the semi market equilibrium. In this paper, we show that maximizing the total utility of the buyers in satisfying the semi market equilibrium is NP-hard and give a 1.5-approximation algorithm for this optimization problem. Moreover, in the market, a buyer may get more utility by misreporting his information. We consider the situation that a buyer may misreport his preference and prove that the incentive ratio, the percentage of the improvement by misreporting the information, is upper bounded by 1.618.
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Acknowledgement
This research is supported by Major Scientific and Technological Special Project of Guizhou Province (20183001), China’s NSFC grants (No. 61433012, 71361003, 71461003), Shenzhen research grant (No. KQJSCX20180330170311901, JCYJ 20180305180840138 and GGFW2017073114031767), Hong Kong GRF-17208019, Shenzhen Discipline Construction Project for Urban Computing and Data Intelligence, Natural Science Foundations of Guizhou Province (No. [2018] 3002) and the Key Science and Technology Foundation of the Education Department of Hebei Province, China (ZD2019021)
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Li, P., Hua, Q., Hu, Z., Ting, HF., Zhang, Y. (2019). Approximation Algorithm and Incentive Ratio of the Selling with Preference. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_26
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DOI: https://doi.org/10.1007/978-3-030-36412-0_26
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