Algorithmic Information Disclosure in Optimal Auctions: NP-Hardness and PTAS

Kernekoncepter

The authors explore the complexity of designing optimal auctions with information disclosure, proving NP-hardness and proposing a PTAS for computing optimal joint designs.

Resumé

The paper delves into the challenges of designing optimal auctions with information disclosure, showcasing NP-hardness when considering signal structures. It introduces a PTAS for computing optimal joint designs with minimal loss in expected revenue. The study emphasizes the importance of regularity in virtual value distributions and proposes dynamic programming algorithms for efficient computation.
The content discusses the complexities of auction design with information disclosure, highlighting challenges in joint design problems. It presents a novel approach to approximate optimal solutions efficiently while maintaining regularity in virtual value distributions. The paper provides insights into computational aspects of auction mechanisms with information disclosure.
Key points include:

Introduction to joint design problem in auctions.
Challenges posed by signal structures and NP-hardness.
Proposal of a PTAS for computing optimal solutions.
Emphasis on regularity in virtual value distributions.
Dynamic programming algorithms for efficient computation.

Statistik

Our main result is a polynomial-time approximation scheme (PTAS) for computing the optimal joint design with at most an ε multiplicative loss in expected revenue.
We show that the worst-case multiplicative gap between optimal welfare and revenue is at most e/(e - 1) for all valuation distributions.
The seller can significantly reduce the information rent of agents by providing partial information, ensuring revenue that is at least 1 - 1/e of the optimal welfare.

Citater

"In these applications, sellers can jointly design their advertising strategies and subsequent auction mechanisms."
"Our main result is a polynomial-time approximation scheme (PTAS) for computing the optimal joint design."

Vigtigste indsigter udtrukket fra

Algorithmic Information Disclosure in Optimal Auctions

by Yang Cai,Yin... kl. arxiv.org 03-14-2024

https://arxiv.org/pdf/2403.08145.pdf

Dybere Forespørgsler

How does the proposed PTAS algorithm compare to existing methods

The proposed PTAS algorithm for the OPTIMAL k-SIGNAL problem is a significant advancement in computational auction theory. Compared to existing methods, the PTAS offers a polynomial-time approximation scheme that computes an optimal solution with at most an ε multiplicative loss in expected revenue. This means that the algorithm can efficiently find nearly optimal solutions for joint design problems where the seller can design both signal structures and selling mechanisms. By leveraging dynamic programming and discretization techniques, the PTAS provides a systematic approach to computing implementable pairs of distributions and compensation terms, ultimately maximizing virtual welfare while ensuring regularity in induced value distributions.

What implications does regularity in virtual value distributions have on auction outcomes

Regularity in virtual value distributions plays a crucial role in determining auction outcomes. In auctions with regular valuation profiles, where virtual values are non-decreasing with respect to actual valuations, it becomes easier to optimize revenue by designing appropriate signal structures and mechanisms. Regularity ensures that buyers' incentives align with their true values post-signal disclosure, leading to more efficient auctions. The presence of regular induced value distributions simplifies computations by allowing for streamlined algorithms like dynamic programming to maximize revenue equivalence through virtual welfare maximization.

How might advancements in computational complexity impact future auction designs

Advancements in computational complexity have profound implications for future auction designs. With the development of algorithms like PTAS for joint design problems in auctions, sellers can now efficiently compute near-optimal solutions even when faced with NP-hardness challenges. This opens up new possibilities for designing sophisticated auction mechanisms tailored to specific contexts such as advertising strategies or private inspections. Improved computational tools enable sellers to explore complex scenarios involving information disclosure and buyer valuation more effectively, leading to enhanced revenue generation and better market outcomes overall.