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| -rw-r--r-- | project2/main.tex | 18 |
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diff --git a/project2/main.tex b/project2/main.tex index e2f93c2..8497ff6 100644 --- a/project2/main.tex +++ b/project2/main.tex @@ -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} |