From 57cccf4b7006f08acddce23221338558dc0e7096 Mon Sep 17 00:00:00 2001
From: Paul <Paul@Pauls-MacBook-Air.local>
Date: Mon, 11 May 2015 19:01:35 -0400
Subject: Minor updates

---
 final/main.tex | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

(limited to 'final/main.tex')

diff --git a/final/main.tex b/final/main.tex
index 198b8ab..8f7ffff 100644
--- a/final/main.tex
+++ b/final/main.tex
@@ -32,6 +32,7 @@
 \DeclareMathOperator*{\E}{\mathbb{E}}
 \let\Pr\relax
 \DeclareMathOperator*{\Pr}{\mathbb{P}}
+\DeclareMathOperator*{\I}{\mathcal{I}}
 
 \newcommand{\inprod}[1]{\left\langle #1 \right\rangle}
 \newcommand{\R}{\mathbb{R}}
@@ -43,7 +44,7 @@
 \newtheorem*{goal}{Goal}
 
 \author{Thibaut Horel \and Paul Tylkin}
-\title{Economics 2099 Project}
+\title{Approximate Mechanisms\\ for Ex-Ante Allocation Constraints \\ \vskip0.1in {\sc Economics 2099 Project}}
 \date{Fall 2014}
 \begin{document}
 
@@ -195,7 +196,7 @@ We can now formally describe the candidate mechanism.
 \end{center}
     \begin{displaymath}
         \begin{cases}
-            x_i = [t_i \geq p_i],\; p = p_0 + \sum_i p_ix_i &\text{ if} \sum_{i=1}^m (t_i - p_i)^+ \geq p_0 \\
+            x_i = \I[t_i \geq p_i],\; p = p_0 + \sum_i p_ix_i &\text{ if} \sum_{i=1}^m (t_i - p_i)^+ \geq p_0 \\
             x_i = 0\text{ for all $i$},\; p = 0&\text{ otherwise }
         \end{cases}
     \end{displaymath}
@@ -203,8 +204,8 @@ We can now formally describe the candidate mechanism.
 \end{minipage}
 }
 \end{center}
-where we used the Iverson bracket notation $[P]$ to denote the indicator
-variable of predicate $P$.
+where we use the notation $\I[\text{expression}]$ to denote the indicator
+variable for the expression, which takes on value 1 when the expression is true and 0 otherwise.
 
 We note that this mechanism is exactly the $\beta$-bundle mechanism from
 \cite{yao}, even though the interpretation in terms of entrance fee plus posted
-- 
cgit v1.2.3-70-g09d2

