Robust Mechanism Design with Limited Information

Project: Research

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Revenue maximization when selling a single item to a single buyer with private valuation is an important topic in mechanism design and is a fundamental building block for more complicated models that involve multiple items or multiple interacting buyers. Its applications appear in a rich range of domains including economics, marketing, and revenue management. A well-designed selling mechanism should be individually rational such that the buyer is willing to participate in the mechanism and at the same time, be incentive-compatible such that no buyer would misreport his valuation. It is well known that as long as the seller knows the buyer's valuation distribution, the strategy of posting a fixed price, named the posted price mechanism, is then optimal. In practice, however, the distribution of the buyer's valuation is rarely known precisely. Rather, the seller often only has a confident estimation of certain statistics, such as maximum and mean, of the buyer's valuation, or a collection of historical data. In such acase, optimality of the posted price mechanism can be fragile---if the seller does not have full information about the buyer's valuation distribution, the seller may achieve a higher revenue if using a selling mechanism beyond the posted price mechanism. Thismotivates us to study the general problem of finding a robust selling mechanism when the seller has limited information on the valuation distribution. In this project, we adopt the robust optimization framework and assume the seller merely knows that the buyer's valuation distribution belongs to an information set of probability distributions that can have its own emphasis in characterizing its member distributions. The seller then seeks an optimal selling mechanism that performs the best with respect to the most adverse distribution that may arise from the information set. We plan to explore this problem with single-buyer and single-item as a starting step and then extend along the following directions. First, the seller can follow different decision criteria (such as the Hurwicz criterion or regret criterion) to guide her decision-making under uncertainty. Second, there could potentially be multiple buyers competing for multiple items through an auction. Third, is there any easy-to-implement heuristic with performance guarantees? Finally, we are keen on applying our theoretical results into practical problems such as online advertising. 


Project number9043424
Grant typeGRF
Effective start/end date1/01/23 → …