[Paper Review] From Bayesian to Crowdsourced Bayesian Auctions.

Jing Chen, Bo Li+1 more|arXiv (Cornell University)|Feb 5, 2017

Auction Theory and Applications48 references3 citations

TL;DR

This paper introduces crowdsourced Bayesian auctions that relax the common prior assumption by distributing knowledge of bidders' value distributions across players and the seller. It proposes 2-step dominant-strategy truthful mechanisms for unit-demand and additive auctions that achieve revenue approaching 100% of optimal Bayesian mechanisms as knowledge increases, showing the common prior assumption is nearly without loss in revenue when knowledge is crowdsourced.

ABSTRACT

A strong assumption in Bayesian mechanism design is that the distributions of the players' private types are common knowledge to the designer and the players--the common prior assumption. An important problem that has received a lot of attention in both economics and computer science is to repeatedly weaken this assumption in game theory--the Wilson's Doctrine. In this work we consider, for the first time in the literature, multi-item auctions where the knowledge about the players' value distributions is scattered among the players and the seller. Each one of them privately knows some or none of the value distributions, no constraint is imposed on who knows which distributions, and the seller does not know who knows what. In such an unstructured information setting, we design mechanisms for unit-demand and additive auctions, whose expected revenue approximates that of the optimal Bayesian mechanisms by crowdsourcing the players' and the seller's knowledge. Our mechanisms are 2-step dominant-strategy truthful and the revenue increases gracefully with the amount of knowledge the players have. In particular, the revenue starts from a constant fraction of the revenue of the best known dominant-strategy truthful Bayesian mechanisms, and approaches 100 percent of the later when the amount of knowledge increases. Our results greatly improve the literature on the relationship between the amount of knowledge in the system and what mechanism design can achieve. In some sense, our results show that the common prior assumption is without much loss of generality in Bayesian auctions if one is willing to give up a fraction of the revenue.

Motivation & Objective

• To address the strong common prior assumption in Bayesian mechanism design, where all agents must know the prior distributions of others' values.
• To model a realistic setting where knowledge about value distributions is unstructured and scattered among bidders and the seller.
• To design truthful mechanisms that leverage this distributed knowledge to approximate the revenue of optimal Bayesian mechanisms.
• To quantify how revenue improves as the amount of distributed knowledge increases, showing graceful convergence to optimal revenue.

Proposed method

• Designs a 2-step mechanism where bidders report their private knowledge about value distributions, and the seller uses this information to compute allocation and payments.
• Employs dominant-strategy truthfulness by ensuring that truthful reporting of knowledge is optimal regardless of others' actions.
• Uses a Bayesian-optimal mechanism as a benchmark and compares revenue against it under varying levels of distributed knowledge.
• Applies a revenue approximation framework that bounds the performance of the mechanism relative to the optimal Bayesian mechanism.
• Introduces a knowledge aggregation protocol that combines partial priors from bidders and the seller to form a global estimate of value distributions.
• Analyzes the mechanism’s performance in terms of revenue approximation, showing it improves monotonically with the total amount of distributed knowledge.

Experimental results

Research questions

• RQ1 How can Bayesian mechanism design be extended when the common prior assumption is violated and knowledge is distributed among bidders and the seller?
• RQ2 To what extent can revenue in multi-item auctions be approximated when only partial knowledge of value distributions is available?
• RQ3 Can truthful mechanisms be designed in this unstructured knowledge setting that still achieve high revenue?
• RQ4 How does the revenue of the proposed mechanism scale with the total amount of distributed knowledge?
• RQ5 Is the common prior assumption necessary for high-revenue mechanisms, or can it be relaxed with minimal revenue loss?

Key findings

• The proposed mechanisms are dominant-strategy truthful, ensuring that truthful reporting of knowledge is optimal for all participants.
• The revenue of the mechanism starts at a constant fraction of the optimal Bayesian mechanism’s revenue when little knowledge is available.
• As the total amount of distributed knowledge increases, the mechanism’s revenue approaches 100% of the optimal Bayesian mechanism’s revenue.
• The revenue increases monotonically and gracefully with the amount of knowledge, showing a smooth trade-off between information availability and performance.
• The results demonstrate that the common prior assumption imposes little loss in revenue if one allows for a small fraction of revenue loss in exchange for relaxed knowledge requirements.