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authorThibaut Horel <thibaut.horel@gmail.com>2013-09-22 18:28:41 -0400
committerThibaut Horel <thibaut.horel@gmail.com>2013-09-22 18:28:41 -0400
commitc7ca7fb461ec2044f8aefcedfcd903d8b5945fc1 (patch)
treeedab2ce716cf642bebbef2c7902c4a322e8fc03b /appendix.tex
parent560eb3da4a23ed3317f8678688f2a55fc7d3c1bf (diff)
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@@ -880,7 +880,7 @@ Placing the expression of $C$ in \eqref{eq:bound1} and \eqref{eq:bound2}
gives the approximation ratio in \eqref{approxbound}, and concludes the proof
of Theorem~\ref{thm:main}.\hspace*{\stretch{1}}\qed
-Finally, we prove the lower bound stated in Theorem~\ref{thm:main}
+Finally, we prove the lower bound stated in Theorem~\ref{thm:main}.
Suppose, for contradiction, that such a mechanism exists. From Myerson's Theorem \cite{myerson}, a single parameter auction is truthful if and only if the allocation function is monotone and agents are paid theshold payments. Consider two
experiments with dimension $d=2$, such that $x_1 = e_1=[1 ,0]$, $x_2=e_2=[0,1]$
and $c_1=c_2=B/2+\epsilon$. Then, one of the two experiments, say, $x_1$, must