Strategy-proof Selling: a Geometric Approach

Mridu Prabal Goswami

Papers from arXiv.org

Abstract: We consider one buyer and one seller. For a bundle $(t,q)\in [0,\infty[\times [0,1]=\mathbb{Z}$, $q$ either refers to the wining probability of an object or a share of a good, and $t$ denotes the payment that the buyer makes. We define classical and restricted classical preferences of the buyer on $\mathbb{Z}$; they incorporate quasilinear, non-quasilinear, risk averse preferences with multidimensional pay-off relevant parameters. We define rich single-crossing subsets of the two classes, and characterize strategy-proof mechanisms by using monotonicity of the mechanisms and continuity of the indirect preference correspondences. We also provide a computationally tractable optimization program to compute the optimal mechanism. We do not use revenue equivalence and virtual valuations as tools in our proofs. Our proof techniques bring out the geometric interaction between the single-crossing property and the positions of bundles $(t,q)$s. Our proofs are simple and provide computationally tractable optimization program to compute the optimal mechanism. The extension of the optimization program to the $n-$ buyer environment is immediate.

Date: 2024-06, Revised 2024-07
New Economics Papers: this item is included in nep-des and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2406.12279 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2406.12279

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().