project2/main.tex


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\documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{amsmath,amsfonts,amsthm}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem*{goal}{Goal}

\author{Thibaut Horel \and Paul Tylkin}
\title{Economics 2099 Project}

\begin{document}

\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}

In \cite{babaioff}, the authors describe a setting with a monopolist seller, offering $n$ heterogeneous goods, and a single buyer. 
\cite{hart}
\cite{hartline}
\cite{yao} 

\bibliographystyle{abbrv}
\bibliography{main}
\end{document}