Minor updates

1 files changed, 3 insertions, 3 deletions

diff --git a/final/main.tex b/final/main.tex
index 8f7ffff..3816d4a 100644
--- a/final/main.tex
+++ b/final/main.tex
@@ -165,7 +165,7 @@ $\gamma$ is a constant which is at least $\frac{1}{2}$.
 
 Given the simplicity of posted-price mechanisms and the fact that they are
 optimal in the single-agent single-item setting (for a regular distribution
-$F$), we would like a mechanism as close as possible to posted-price.
+$F$), it would be desirable to obtain a mechanism as close as possible to posted-price.
 Unfortunately, Hart and Nisan \cite{hart-nisan} showed that even in the
 unconstrained, regular case, no posted-price mechanism for the single-agent
 problem has an approximation ratio better than $\Omega(\log n)$.
@@ -178,11 +178,11 @@ This is essentially the concept of a two-part tariff, as discussed in
 
 Note that as written above, the candidate mechanism is not individually
 rational because the agent gets charged $p_0$ regardless of her type. To
-restore individual rationality, we need to have the agent pay only when:
+restore individual rationality, we need to have the agent pay only when
 \begin{displaymath}
     \sum_{i=1}^m (t_i - p_i)^+ \geq p_0
 \end{displaymath}
-where we used the notation $(x)^+\eqdef\max\{x, 0\}$, so that the
+where we used the notation $(x)^+\eqdef\max(x, 0)$, so that the
 above inequality could also be written as $$\sum_{i: t_i\geq p_i} (t_i- p_i)\geq p_0.$$
 
 We can now formally describe the candidate mechanism.