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authorStratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>2013-07-03 10:17:46 -0700
committerStratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>2013-07-03 10:17:46 -0700
commita146d718108b39c2b5323245c399577f9cf1f14e (patch)
tree2d37b2d932e647bcde383e8789f4260672534865 /problem.tex
parent755c7cc3dd07c3b081be23966f55a0066cdd4271 (diff)
downloadrecommendation-a146d718108b39c2b5323245c399577f9cf1f14e.tar.gz
paper
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@@ -208,10 +208,10 @@ Ideally, we would like the allocation $S$ to be of maximal value; however, truth
%time in the number of agents $n$. %\thibaut{Should we say something about the black-box model for $V$? Needed to say something in general, but not in our case where the value function can be computed in polynomial time}.
\end{itemize}
+\begin{comment}
As noted in \cite{singer-mechanisms, chen}, budget feasible reverse auctions are \emph{single parameter} auctions: each agent has only one
private value (namely, $c_i$). As such, Myerson's Theorem \cite{myerson} gives
a characterization of truthful mechanisms. We use the following variant of the theorem: %NEEDS TO BE FIXED
-\begin{comment}
\begin{lemma}[\citeN{myerson}]\label{thm:myerson}
\sloppy A normalized mechanism $\mathcal{M} = (S,p)$ for a single parameter auction is
truthful iff:
@@ -224,7 +224,6 @@ c_{-i})$ implies $i\in S(c_i', c_{-i})$, and (b)
agents are paid \emph{threshold payments}, \emph{i.e.}, for all $i\in S(c)$, $p_i(c)=\inf\{c_i': i\in S(c_i', c_{-i})\}$.
%\end{enumerate}
\end{lemma}
-\end{comment}
\begin{lemma}[\citeN{myerson}]\label{thm:myerson-variant}
\sloppy A normalized mechanism $\mathcal{M} = (S,p)$ for a single parameter auction is
@@ -241,7 +240,7 @@ Myerson's Theorem
% is particularly useful when designing a budget feasible truthful mechanism, as it
allows us to focus on designing a monotone allocation function $S$. Then, the
mechanism will be truthful as long as we give each agent her threshold payment---the caveat being that the latter need to sum to a value below $B$.
-
+\end{comment}
\begin{comment}
\subsection{Budget Feasible Experimental Design}