From ee9252a6175d5333ae1ea9bb2bf0b8b1b3c69210 Mon Sep 17 00:00:00 2001
From: Paul <Paul@Pauls-MacBook-Air.local>
Date: Tue, 12 May 2015 16:53:45 -0400
Subject: Added details on Yao's BGR approach

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

(limited to 'final/main.tex')

diff --git a/final/main.tex b/final/main.tex
index 5508b59..ec3e253 100644
--- a/final/main.tex
+++ b/final/main.tex
@@ -298,7 +298,9 @@ a mechanism is said to be $p$-exclusive if $x_i = 0$ whenever $p_i > t_i$. This
 is essentially saying that there is a reserve price for each item.
 
 The notion of $p$-exclusivity introduced\footnote{\citep{yao} actually uses the notation $\beta$-exclusive for the same thing, but we thought that $p$ was a more natural choice.} by \citep{yao} was crucial in his reduction
-from the $k$-item $m$-buyer setting to the $k$-item single buyer setting. $p$-exclusivity
+from the $k$-item $m$-buyer setting to the $k$-item single buyer setting. He describes a mechanism known as \emph{Best-Guess Reduction}, which conducts $m$ single-buyer $k$-item auctions, using an IR-IC $p$-exclusive mechanism, for a particular value of $p$ drawn from the joint bid distribution over all buyers conditioned on the bids of all other buyers, and then combines this with the Vickrey second-price auction, showing that this mechanism has revenue that is a constant approximation to the optimal $k$-item, $m$-buyer mechanism. He then defines another mechanism, \emph{Second-Price Bundling}, which is meant to heuristically approximate this combined mechanism, and shows that its revenue is also a constant approximation to the optimal mechanism.
+
+$p$-exclusivity
 can easily be enforced in the optimization we formulated in Section~\ref{sec:intro},
 by adding the following non-linear constraints:
 \begin{displaymath}
-- 
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