NDLI: On the Complexity of Optimal Lottery Pricing and Randomized Mechanisms

Content Provider	IEEE Xplore Digital Library
Author	Xi Chen Diakonikolas, I. Orfanou, A. Paparas, D. Xiaorui Sun Yannakakis, M.
Copyright Year	2015
Description	Author affiliation: Sch. of Inf., Univ. of Edinburgh, Edinburgh, UK (Diakonikolas, I.) \|\| Comput. Sci. Dept., Columbia Univ., New York, NY, USA (Xi Chen; Orfanou, A.; Paparas, D.; Xiaorui Sun; Yannakakis, M.)
Abstract	We study the optimal lottery problem and the optimal mechanism design problem in the setting of a single unit-demand buyer with item values drawn from independent distributions. Optimal solutions to both problems are characterized by a linear program with exponentially many variables. For the menu size complexity of the optimal lottery problem, we present an explicit, simple instance with distributions of support size 2, and show that exponentially many lotteries are required to achieve the optimal revenue. We also show that, when distributions have support size 2 and share the same high value, the simpler scheme of item pricing can achieve the same revenue as the optimal menu of lotteries. The same holds for the case of two items with support size 2 (but not necessarily the same high value). For the computational complexity of the optimal mechanism design problem, we show that unless the polynomial-time hierarchy collapses (more exactly, PNP = P#P), there is no universal efficient randomized algorithm to implement an optimal mechanism even when distributions have support size 3.
Starting Page	1464
Ending Page	1479
File Size	313896
Page Count	16
File Format	PDF
ISBN	9781467381918
ISSN	02725428
DOI	10.1109/FOCS.2015.93
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Pricing Complexity theory Standards Algorithm design and analysis Polynomials Additives Cost accounting unit-demand buyer Lottery pricing optimal mechanism design
Content Type	Text
Resource Type	Article

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