this is for holding javascript data
Sébastien Rouillon added Altogether_this_shows_that_the__.tex
over 8 years ago
Commit id: ae28f11741cca027fe8a7c1ccd8c4ec1a1db9591
deletions | additions
diff --git a/Altogether_this_shows_that_the__.tex b/Altogether_this_shows_that_the__.tex
new file mode 100644
index 0000000..c01d187
--- /dev/null
+++ b/Altogether_this_shows_that_the__.tex
...
Altogether, this shows that the Nash equilibrium of the contest game is unique and interior.\footnote{It is worth noting that this result is not specific to the uniform distribution of damage. In fact, it remains true for any cumulative distribution of damage $F\left(\delta\right)$ such that $\int\nolimits _{k}^{1}\left(\delta-k\right)dF\left(\delta\right)>0$. We thank David Malueg for pointing us this point.} Solving (\ref{eq:focE}), we obtain that the equilibrium efforts of lobbies $I$ and $E$ equal
\begin{equation}
x^{\ast}\left(\delta\right)=
\sqrt{\left(b-\min\left(\delta,k\right)\right)y^{*}}-y^{*}\mbox{, for all }\delta,
\label{eq:x*}
\end{equation}
\begin{equation}
y^{\ast}=
\left(\frac{\left(1-k\right)^{2}}{2\left(b-k\right)+\left(1-k\right)^{2}}\right)^{2}\left(b-k\right).
\label{eq:y*}
\end{equation}
