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| -rw-r--r-- | project2/main.tex | 21 |
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diff --git a/project2/main.tex b/project2/main.tex index 8b29b5b..daf7411 100644 --- a/project2/main.tex +++ b/project2/main.tex @@ -123,10 +123,6 @@ for the multi-agent problem which is a $\gamma\cdot\alpha$ approximation to the revenue-optimal mechanism where $\gamma$ is a constant which is at least $\frac{1}{2}$. - -To provide some more intuition about this, we assume that the buyer is charged a price $p_0$ to participate in the mechanism, -and then is offered a menu of goods with prices $p_1,...,p_m$. The buyer's utility over the goods is additive, as above. However, there is an ex-ante constraint of being allocated a given good $i$, given by $\hat{x}_i$. For each good, if the buyer is allocated the good, which he is with probability $x_i \leq \hat{x}_i$, then he pays $p_i$; otherwise, he pays nothing. This is essentially the concept of a two-part tariff, as discussed in \cite{armstrong}. - It is interesting to consider two specific cases for which we already have an answer to our problem: \begin{itemize} @@ -141,15 +137,14 @@ answer to our problem: which TODO:cite provides a 2 approximation to $R\left( \left(\frac{1}{m},\ldots,\frac{1}{m}\right)\right)$. \end{itemize} -\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} -\cite{armstrong} -\cite{alaei} +In the general case, a candidate simple mechanism suggested by Jason Hartline +is the following: the buyer is charged a price $p_0$ to participate in the +mechanism, and then is offered a menu of goods with prices $p_1,...,p_m$. +However, there is an ex-ante constraint of being allocated a given good $i$, +given by $\hat{x}_i$. For each good, if the buyer is allocated the good, which +he is with probability $x_i \leq \hat{x}_i$, then he pays $p_i$; otherwise, he +pays nothing. This is essentially the concept of a two-part tariff, as +discussed in \cite{armstrong}. \bibliographystyle{abbrv} \bibliography{main} |