From 565ca81772eedfceda0d3ea7b69174718e9f6cc5 Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Wed, 31 Oct 2012 00:38:32 -0700
Subject: stuff

---
 main.tex | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 0c2b633..94b2a47 100644
--- a/main.tex
+++ b/main.tex
@@ -1,3 +1,17 @@
+
+\subsection{D-Optimality Criterion}
+\begin{lemma}
+For any $M>0$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
+\end{lemma}
+\begin{proof}
+\input{proof_of_lower_bound1}
+\end{proof}
+
+This motivates us to look at $$V(S) = \log\det(I_d+\T{X_S}X_S).$$ Interesting for many reasons. Experiment with basis points $e_1$,\ldots,$e_d$, already given for free. Connections to Baysian optimal experiment design: we explore this more in Section~\ref{...}. Close to $D$-optimality criterion when number of experiments is large. Important properties $V(\emptyset)=0$, $V$ is submodular, allows us to exploit the arsenal in our disposal to deal with budget feasible mechanism design for submodular functions.
+
+\subsection{Truthful, Constant Approximation Mechanism}
+
+
 In this section we present a mechanism for the problem described in
 section~\ref{sec:auction}. Previous works on maximizing submodular functions
 \cite{nemhauser, sviridenko-submodular} and desiging auction mechanisms for
-- 
cgit v1.2.3-70-g09d2

