Summary: Characterization of Revenue Equivalence
July 1, 2008
The property of an allocation rule to be implementable in dominant strategies by a unique
payment scheme is called revenue equivalence. We give a characterization of revenue equiv-
alence based on a graph theoretic interpretation of the incentive compatibility constraints.
The characterization holds for any (possibly infinite) outcome space and many of the known
results are immediate consequences. Moreover, revenue equivalence can be identified in cases
where existing theorems are silent.
One of the most important results of auction theory is the Revenue Equivalence Theorem.
Subject to certain reasonable assumptions, it concludes that a variety of different auctions
generate the same expected revenue for the seller. Klemperer (1999) writes that "much of
auction theory can be understood in terms of this theorem.....". Hence the long line of papers
that have attempted to relax the sufficient conditions under which revenue equivalence holds.
The present paper provides necessary and sufficient conditions on the underlying primitives for