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Diffstat (limited to 'final/main.tex')
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1 files changed, 6 insertions, 2 deletions
diff --git a/final/main.tex b/final/main.tex index ce13499..108d569 100644 --- a/final/main.tex +++ b/final/main.tex @@ -300,7 +300,11 @@ price. Then we have: As noted by \citep{yao}, the above mechanism $\M$ has the additional property of being $p$-exclusive, where $p$-exclusivity\footnote{\citep{yao} actually uses the +<<<<<<< HEAD +notation $\beta$-exclusive for the same thing, but use $p$ here to have +======= notation $\beta$-exclusive for the same thing, but we use $p$ here to have +>>>>>>> 8f545e3ba41dbe4d5b686d4e9311243c94fc9b91 consistent notations.} is defined as follows: for a vector $p = (p_1,\dots,p_m)$ a mechanism is said to be $p$-exclusive if $x_i = 0$ whenever $p_i > t_i$. This is essentially saying that there is a reserve price for each item. @@ -322,12 +326,12 @@ Lemma. = \big(F^{-1}(1-p_1), \dots, F^{-1}(1-p_m)\big).$$ \end{lemma} -\section{$n$-to-1 Bidders Reductions} +\section{$m$-to-1 Bidders Reductions} The goal of this section is to compare the two ways of constraining the single buyer problem that we discussed: namely $p$-exclusivity and ex-ante allocation constraints and draw a parallel in how these two notions are used to construct -$n$-to-1 bidders reductions in \citep{yao} and \citep{alaei} respectively. +$m$-to-1 bidders reductions in \citep{yao} and \citep{alaei} respectively. The notion of $p$-exclusivity introduced by \citep{yao} was crucial in his |