Abstract
We consider the design of an optimal mechanism for a seller selling two items to a single buyer so that the expected revenue to the seller is maximized. The buyer’s valuation of the two items is assumed to be the uniform distribution over an arbitrary rectangle \([c_1,c_1+b_1]\times [c_2,c_2+b_2]\) in the positive quadrant. The solution to the case when \((c_1,c_2)=(0,0)\) was already known. We provide an explicit solution for arbitrary nonnegative values of \((c_1,c_2,b_1,b_2)\). We prove that the optimal mechanism is to sell the two items according to one of eight simple menus. We also prove that the solution is deterministic when either \(c_1\) or \(c_2\) is beyond a threshold. Finally, we conjecture that our methodology can be extended to a wider class of distributions. We also provide some preliminary results to support the conjecture.
Supported by the Defence Research and Development Organisation, Govt. of India.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Daskalakis, C., Deckelbaum, A., Tzamos, C.: Mechanism design via optimal transport. In: The 14th ACM Conference on Electronic Commerce, EC 2013, pp. 269–286. ACM, New York (2013)
Daskalakis, C., Deckelbaum, A., Tzamos, C.: Strong duality for a multiple-good monopolist (2014). http://arxiv.org/pdf/1409.4150v1.pdf
Daskalakis, C., Deckelbaum, A., Tzamos, C.: Strong duality for a multiple-good monopolist. In: The 16th ACM Conference on Economics and Computation, EC 2015, pp. 449–450. ACM, New York (2015)
Giannakopoulos, Y., Koutsoupias, E.: Duality and optimality of auctions for uniform distributions. In: The 15th ACM Conference on Economics and Computation, EC 2014, pp. 259–276. ACM, New York (2014)
Giannakopoulos, Y., Koutsoupias, E.: Selling two goods optimally. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 650–662. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47666-6_52
Manelli, A.M., Vincent, D.R.: Bundling as an optimal selling mechanism for a multiple-good monopolist. J. Econ. Theory 127(1), 1–35 (2006)
Manelli, A.M., Vincent, D.R.: Multidimensional mechanism design: revenue maximization and the multiple-good monopoly. J. Econ. Theory 137(1), 153–185 (2007)
Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)
Pavlov, G.: Optimal mechanism for selling two goods. B.E. J. Theor. Econ. 11(1), 1–35 (2011)
Rochet, J.C., Choné, P.: Ironing, sweeping, and multidimensional screening. Econometrica 66(4), 783–826 (1998). http://www.jstor.org/stable/2999574
Rochet, J.C.: A necessary and sufficient condition for rationalizability in a quasi-linear context. J. Math. Econ. 16(2), 191–200 (1987)
Wang, Z., Tang, P.: Optimal mechanisms with simple menus. In: The 15th ACM Conference on Economics and Computation, pp. 227–240. ACM (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag GmbH Germany
About this paper
Cite this paper
D., T., Sundaresan, R., Narahari, Y. (2016). Optimal Mechanism for Selling Two Items to a Single Buyer Having Uniformly Distributed Valuations. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-662-54110-4_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-54109-8
Online ISBN: 978-3-662-54110-4
eBook Packages: Computer ScienceComputer Science (R0)