Tight revenue gaps among simple and optimal mechanisms

Consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, who independently draw their values from regular and publicly known distributions. There are four mechanisms widely studied in the literature and widely used in practice: Myerson Auction (OPT), Sequential Posted Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR), and Anonymous Pricing (AP). OPT is revenue-optimal but complicated, which also experiences several practical issues such as fairness. AP is the simplest mechanism, but also generates the lowest revenue among these four mechanisms. SPM and AR are of intermediate complexity and revenue. A quantitative approach to comparing the relative power of these mechanisms is to study their revenue gaps, each of which is defined as the largest ratio between the revenues from a pair of mechanisms. This letter surveys some recent developments on establishing tight revenue gaps, and highlights some open questions.