Thirumulanathan, D and Sundaresan, R and Narahari, Y (2019) On optimal mechanisms in the two-item single-buyer unit-demand setting. In: Journal of Mathematical Economics, 82 . pp. 31-60.
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Abstract
We consider the problem of designing a revenue-optimal mechanism in the two-item, single-buyer, unit-demand setting when the buyer's valuations, (z 1 ,z 2 ), are uniformly distributed in an arbitrary rectangle c,c+b 1 �c,c+b 2 in the positive quadrant. We provide a complete and explicit solution for arbitrary nonnegative values of (c,b 1 ,b 2 ). We identify five simple structures, each with at most five (possibly stochastic) menu items, and prove that the optimal mechanism has one of the five structures. We also characterize the optimal mechanism as a function of b 1 ,b 2 , and c. When c is low, the optimal mechanism is a posted price mechanism with an exclusion region; when c is high, it is a posted price mechanism without an exclusion region. Our results are the first to show the existence of optimal mechanisms with no exclusion region, to the best of our knowledge. © 2019 Elsevier B.V.
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of Mathematical Economics |
| Publisher: | ELSEVIER SCIENCE BV |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 26 Mar 2019 07:53 |
| Last Modified: | 25 Aug 2022 06:45 |
| URI: | https://eprints.iisc.ac.in/id/eprint/61990 |
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