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Diffstat (limited to 'final')
| -rw-r--r-- | final/main.tex | 10 |
1 files changed, 6 insertions, 4 deletions
diff --git a/final/main.tex b/final/main.tex index 1ecfbca..8ac2bbe 100644 --- a/final/main.tex +++ b/final/main.tex @@ -139,9 +139,10 @@ a 6-approximation to $\Rev((1,...,1),F)$. The main question underlying this work can then be formulated as: -\paragraph{Question.} \emph{Given an ex-ante allocation constraint $\hat{x}$ and a type distribution $F$, is -there a simple mechanism whose ex-ante allocation rule is upper-bounded by -$\hat{x}$ and whose revenue is a constant approximation to $\Rev(\hat{x},F)$?} +\paragraph{Question.} \emph{Given an ex-ante allocation constraint $\hat{x}$ +and a type distribution $F$, is there a simple mechanism whose ex-ante +allocation rule is upper-bounded by $\hat{x}$ and whose revenue is a constant +approximation to $\Rev(\hat{x},F)$?} \subsection{Examples and Motivations} @@ -277,7 +278,8 @@ price. Then we have: \begin{proof} The second inequality is the main result from \citep{babaioff}; we will - thus only prove the first inequality. + thus only prove the first inequality, which holds even without the + assumption that $F$ is a product distribution. In the specific case where $\hat{v} = (0,\hat{v}_1,\dots,\hat{v}_m)$, \emph{i.e} $\hat{v}_0 = 0$, there is no entrance fee and the two-part |