Year: 2015
Type: conference-paper
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.
DOI: 10.1109/focs.2015.93
Institutions: Columbia University, University of Edinburgh
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: AF: Small: Computational Aspects of Markets, Equilibria, and Fixed Points, CAREER: Bridging Game Theory, Economics and Computer Science: Equilibria, Fixed Points, and Beyond, G6615897007, AF: Small: On the Complexity of Optimal Pricing and Mechanism Design, Sublinear Algorithms for Approximating Probability Distributions
OpenAlex ID: W2219868088