The seller wants to sell an item to n buyers such that the buyers' valuation distribution is from a given class (i.i.d., mixtures of i.i.d., affiliated and exchangeable, exchangeable, and all distributions) and the seller minimizes worst-case regret. The first three classes admit the same minimax regret, decreasing in n, while the last two have the same minimax regret equal to that of the case n = 1. Across all settings, the optimal mechanisms are all second-price auctions with random reserve.

We study a new selling mechanism in online display advertising markets that combines both guarantee contracts (GC) and real-time bidding (RTB) and allow advertisers to strategically choose between these two channels. Despite the complexity due to the advertisers’ strategic behaviour and the auctions, we are able to obtain the closed-form solution and show that combining GC and RTB can generate more revenue for the publisher, compared to the case when only RTB or GC is used.

We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share her (verifiable) data in exchange for a monetary reward or services, but at the same time has a (private) heterogeneous privacy cost which we quantify using differential privacy.