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Diffstat (limited to 'final/main.tex')
| -rw-r--r-- | final/main.tex | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/final/main.tex b/final/main.tex index 3816d4a..066fabe 100644 --- a/final/main.tex +++ b/final/main.tex @@ -113,7 +113,7 @@ Problem~\ref{eq:opt}: which expresses that the ex-ante allocation probability is upper-bounded by $\hat{x}$. -We use the notation from \cite{alaei} where $R(\hat{x})$ denotes the revenue +We use the notation from \cite{alaei}, where $R(\hat{x})$ denotes the revenue obtained by the optimal mechanism solution to Problem~\ref{eq:opt} with ex-ante allocation constraint $\hat{x}$ given by \eqref{eq:ea}. The main question underlying this work can then be formulated as: @@ -124,8 +124,8 @@ $\hat{x}$ and whose revenue is a constant approximation to $R(\hat{x})$?} \subsection{Examples and Motivations} -\paragraph{}Note that when $\hat{x} = (1,\ldots,1)$, \eqref{eq:ea} does not further -constrain Problem~\ref{eq:opt}, i.e. the constraint is trivially satisfied. In +\paragraph{}Note that when $\hat{x} = (1,\ldots,1)$, the ex-ante allocation constraint \eqref{eq:ea} does not further +constrain the optimization problem given by Equation \ref{eq:opt}, i.e. the constraint is trivially satisfied. In this case, as discussed above, the mechanism described in \cite{babaioff} provides a 6-approximation to $R((1,...,1))$. |