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What fraction of the potential social surplus in an environment can beextracted by a revenue-maximizing monopolist? We investigate this problem inBayesian single-parameter environments with independent private values. Theprecise answer to the question obviously depends on the particulars of theenvironment: the feasibility constraint and the distributions from which thebidders' private values are sampled. Rather than solving the problem inparticular special cases, our work aims to provide universal lower bounds onthe revenue-to-welfare ratio that hold under the most general hypotheses thatallow for non-trivial such bounds.  Our results can be summarized as follows. For general feasibilityconstraints, the revenue-to-welfare ratio is at least a constant times theinverse-square-root of the number of agents, and this is tight up to constantfactors. For downward-closed feasibility constraints, the revenue-to-welfareratio is bounded below by a constant. Both results require the bidders'distributions to satisfy hypotheses somewhat stronger than regularity; we showthat the latter result cannot avoid this requirement.

On the Ratio of Revenue to Welfare in Single-Parameter Mechanism Design