From d5314134066e42e108e13204f45cb3f33f724938 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Tue, 12 May 2015 20:21:47 -0400
Subject: Revert back to n: n is the number of bidders, m the number of items

---
 final/main.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'final/main.tex')

diff --git a/final/main.tex b/final/main.tex
index dfa5914..18d0a30 100644
--- a/final/main.tex
+++ b/final/main.tex
@@ -322,22 +322,22 @@ Lemma.
     = \big(F^{-1}(1-p_1), \dots, F^{-1}(1-p_m)\big).$$
 \end{lemma}
 
-\section{$m$-to-1 Bidders Reductions}
+\section{$n$-to-1 Bidders Reductions}
 
 The goal of this section is to compare the two ways of constraining the single
 buyer problem that we discussed: namely $p$-exclusivity and ex-ante allocation
 constraints and draw a parallel in how these two notions are used to construct
-$m$-to-1 bidders reductions in \citep{yao} and \citep{alaei} respectively.
+$n$-to-1 bidders reductions in \citep{yao} and \citep{alaei} respectively.
 
 
 The notion of $p$-exclusivity introduced by \citep{yao} was crucial in his
-reduction from the $k$-item $m$-buyer setting to the $k$-item single buyer
+reduction from the $k$-item $n$-buyer setting to the $m$-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
+conducts $n$ single-buyer $m$-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
+revenue that is a constant approximation to the optimal $m$-item, $n$-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.
-- 
cgit v1.2.3-70-g09d2

