Revelation Gap for Pricing from Samples
Abstract
This paper considers priorindependent mechanism design, in which a single mechanism is designed to achieve approximately optimal performance on every prior distribution from a given class. Most results in this literature focus on mechanisms with truthtelling equilibria, a.k.a., truthful mechanisms. Feng and Hartline (2018) introduce the revelation gap to quantify the loss of the restriction to truthful mechanisms. We solve a main open question left in Feng and Hartline (2018); namely, we identify a nontrivial revelation gap for revenue maximization. Our analysis focuses on the canonical problem of selling a single item to a single agent with only access to a single sample from the agent's valuation distribution. We identify the samplebid mechanism (a simple nontruthful mechanism) and upperbound its priorindependent approximation ratio by 1.835 (resp. 1.296) for regular (resp. MHR) distributions. We further prove that no truthful mechanism can achieve priorindependent approximation ratio better than 1.957 (resp. 1.543) for regular (resp. MHR) distributions. Thus, a nontrivial revelation gap is shown as the samplebid mechanism outperforms the optimal priorindependent truthful mechanism. On the hardness side, we prove that no (possibly nontruthful) mechanism can achieve priorindependent approximation ratio better than 1.073 even for uniform distributions.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2102.13496
 Bibcode:
 2021arXiv210213496F
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 This paper will appear in Proceedings of the ACM Symposium on Theory of Computing 2021 (STOC'21)