From d0349ca6b30e11915cd95c00e981e712198fb5da Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Wed, 31 Oct 2012 11:19:12 -0700
Subject: lower bound

---
 main.tex | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index e2e7df6..20f500a 100644
--- a/main.tex
+++ b/main.tex
@@ -1,7 +1,9 @@
 
 \subsection{D-Optimality Criterion}
+Ideally, motivated by the $D$-optimality criterion, we would like to design a mechanism that maximizes \eqref{dcrit} within a good approximation ratio. As \eqref{dcrit} may take arbitrarily small negative values, to define a meaningful approximation we consider with the (equivalent) maximization of $V(S) = f(\det\T{X_S}X_S )$, for some increasing, on-to function $f:\reals_+\to\reals_+$. However, the following lower bound implies that such an optimization goal cannot be attained under the costraints of  truthfulness, budget feasibility, and individional rationallity.
+
 \begin{lemma}
-For any $M>0$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
+For any $M>1$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
 \end{lemma}
 \begin{proof}
 \input{proof_of_lower_bound1}
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