Add the properties we seek for mechanisms. Add Myerson's theorem.

1 files changed, 5 insertions, 6 deletions

diff --git a/main.tex b/main.tex
index 324c2f8..53de028 100644
--- a/main.tex
+++ b/main.tex
@@ -125,12 +125,11 @@ We can now state the main result of this section:
 
 \begin{proof}
 \emph{Truthfulness.} The algorithm only describes the allocation rule.
-However, it suffices to prove that the mechanism is monotone, then
-Myerson's theorem (see TODO) ensures us that by paying each allocated
-user his threshold payment yields a truthful mechanism. The proof of
-the monotonicity has already been done in \cite{singer-influence} and
-is given here in lemma~\ref{lemma:monotone} below for the sake of
-completeness.
+However, it suffices to prove that the mechanism is monotone, then Myerson's
+theorem (see theorem~\ref{thm:myerson}) ensures us that by paying each
+allocated user his threshold payment yields a truthful mechanism. The proof of
+the monotonicity has already been done in \cite{singer-influence} and is given
+here in lemma~\ref{lemma:monotone} below for the sake of completeness.
 
 \emph{Budget feasibility.} Thanks to the analysis of the threshold
 payment in \cite{chen}, the budget feasibility follows easily. The