  We consider a fundamental problem in microeconomics: selling a single item to
a number of potential buyers, whose values are drawn from known independent and
regular (not necessarily identical) distributions. There are four widely-used
and widely-studied mechanisms in the literature: {\sf Myerson Auction}~({\sf
OPT}), {\sf Sequential Posted-Pricing}~({\sf SPM}), {\sf Second-Price Auction
with Anonymous Reserve}~({\sf AR}), and {\sf Anonymous Pricing}~({\sf AP}).
  {\sf OPT} is revenue-optimal but complicated, which also experiences several
issues in practice such as fairness; {\sf AP} is the simplest mechanism, but
also generates the lowest revenue among these four mechanisms; {\sf SPM} and
{\sf AR} are of intermediate complexity and revenue. We explore revenue gaps
among these mechanisms, each of which is defined as the largest ratio between
revenues from a pair of mechanisms. We establish two tight bounds and one
improved bound:
  1. {\sf SPM} vs.\ {\sf AP}: this ratio studies the power of discrimination in
pricing schemes. We obtain the tight ratio of $\mathcal{C^*} \approx 2.62$,
closing the gap between $\big[\frac{e}{e - 1}, e\big]$ left before.
  2. {\sf AR} vs.\ {\sf AP}: this ratio measures the relative power of auction
scheme vs.\ pricing scheme, when no discrimination is allowed. We attain the
tight ratio of $\frac{\pi^2}{6} \approx 1.64$, closing the previously known
bounds $\big[\frac{e}{e - 1}, e\big]$.
  3. {\sf OPT} vs.\ {\sf AR}: this ratio quantifies the power of discrimination
in auction schemes, and is previously known to be somewhere between $\big[2,
e\big]$. The lower-bound of $2$ was conjectured to be tight by Hartline and
Roughgarden (2009) and Alaei et al.\ (2015). We acquire a better lower-bound of
$2.15$, and thus disprove this conjecture.
