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Optimal mechanisms for selling two items to a single buyer having uniformly distributed valuations

Thirumulanathan, D and Sundaresan, Rajesh and Narahari, Y (2019) Optimal mechanisms for selling two items to a single buyer having uniformly distributed valuations. In: JOURNAL OF MATHEMATICAL ECONOMICS, 82 . pp. 1-30.

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Official URL: https://dx.doi.org/10.1016/j.jmateco.2019.01.004


We consider the design of a revenue-optimal mechanism when two items are available to be sold to a single buyer whose valuation is uniformly distributed over an arbitrary rectangle c(1), c(1) +b(1)] x c(2), c(2)+b(2)] in the positive quadrant. We provide an explicit, complete solution for arbitrary nonnegative values of (c(1), c(2), b(1), b(2)). We identify eight simple structures, each with at most 4 (possibly stochastic) menu items, and prove that the optimal mechanism has one of these eight structures. We also characterize the optimal mechanism as a function of (c(1), c(2), b(1), b(2)). The structures indicate that the optimal mechanism involves (a) an interplay of individual sale and a bundle sale when c(1) and c(2) are low, (b) a bundle sale when c(1) and c(2) are high, and (c) an individual sale when one of them is high and the other is low. To the best of our knowledge, our results are the first to show the existence of optimal mechanisms with no exclusion region. We further conjecture, based on promising preliminary results, that our methodology can be extended to a wider class of distributions.

Item Type: Journal Article
Additional Information: The copyright for this article belongs to Elsevier B.V.
Keywords: Game theory; Economics; Optimal auctions; Stochastic orders; Convex optimization
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Division of Electrical Sciences > Electrical Communication Engineering
Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited: 20 Jun 2019 16:42
Last Modified: 20 Jun 2019 16:42
URI: http://eprints.iisc.ac.in/id/eprint/62782

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