  Very few exact solutions are known for the monopolist's $k$-item $n$-buyer
maximum revenue problem with additive valuation in which $k, n >1$ and the
buyers $i$ have independent private distributions $F^j_i$ on items $j$. In this
paper we derive exact formulas for the maximum revenue when $k=2$ and $F^j_i$
are any IID distributions on support of size 2, for both the dominant-strategy
(DIC) and the Bayesian (BIC) implementations. The formulas lead to the simple
characterization that, the two implementations have identical maximum revenue
if and only if selling-separately is optimal for the distribution. Our results
also give the first demonstration, in this setting, of revenue gaps between the
two implementations. For instance, if $k=n=2$ and
$Pr\{X_F=1\}=Pr\{X_F=2\}=\frac{1}{2}$, then the maximum revenue in the Bayesian
implementation exceeds that in the dominant-strategy by exactly $2\%$; the same
gap exists for the continuous uniform distribution $X_F$ over $[a, a+1]\cup[2a,
2a+1]$ for all large $a$.
