  We consider the revenue maximization problem of a monopolist via a
non-Myersonian approach that could generalize to multiple items and multiple
buyers. Although such an approach does not lead to any closed-form solution of
the problem, it does provide some insights into this problem from different
angles. In particular, we consider both Bayesian (Bayesian Incentive Compatible
+ Bayesian Individually Rational) and Dominant-Strategy (Dominant-Strategy
Incentive Compatible + ex-post Individually Rational) implementations, where
all the buyers have additive valuations and quasi-linear utilities and all the
valuations are independent across buyers (not necessarily independent across
items).
  The main technique of our approach is to formulate the problem as an LP
(probably with exponential size) and apply primal-dual analysis. We observe
that any optimal solution of the dual program naturally defines the virtual
value functions for the primal revenue maximization problem in the sense that
any revenue-maximizing auction must be a virtual welfare maximizer (cf.
Myerson's auction for a single item [Myerson, 1981]).
  Based on this observation, we characterize a sufficient and necessary
condition for BIC = DSIC, i.e., the optimal revenue of Bayesian implementations
equals to the optimal revenue of dominant-strategy implementations (BRev =
DRev). The condition is if and only if the optimal DSIC revenue DRev can be
achieved by a DSIC and ex-post IR virtual welfare maximizer with
buyer-independent virtual value functions (buyer i's virtual value is
independent of other buyers' valuations). In light of the characterization, we
further show that when all the valuations are i.i.d., it is further equivalent
to that separate-selling is optimal. In particular, it respects one result from
the recent breakthrough work on the exact optimal solutions in the multi-item
multi-buyer setting by Yao [2016].
