From e1f020a9cc90449f403bc25cf2b28488dedd3621 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Thu, 11 Dec 2014 10:44:11 -0500
Subject: Problem statement

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 project2/main.tex | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

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diff --git a/project2/main.tex b/project2/main.tex
index e2f93c2..8497ff6 100644
--- a/project2/main.tex
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@@ -41,6 +41,24 @@
 
 \maketitle
 
+\section{Problem}
+
+We are interested in a multi-item auction for agents with submodular
+preferences.
+
+If we denote by $m$ the number of items, we look at a specific case where the
+type $t$ of an agent is a vector $t=(t_1,\ldots,t_m)$ drawn from a distribution
+$F$ over $\mathbb{R}_+^m$ and for an allocation $x$ and price
+$p$, the utility of the agent is:
+\begin{displaymath}
+    u(t, x, p) = \sum_{S\subseteq 2^m} x(S)g\left(1+\sum_{j\in S} t_j\right)-p
+\end{displaymath}
+where $g$ is a concave function from $\mathbb{R}_+$ to $\mathbb{R}_+$ with
+$g(0) = 0$.
+
+
+\section{Related Work}
+
 \cite{babaioff}
 \cite{yao}
 \cite{hart}
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