deletions | additions       diff --git a/sectionComparison_of.tex b/sectionComparison_of.tex  index 1c31540..01fba7d 100644  --- a/sectionComparison_of.tex  +++ b/sectionComparison_of.tex 
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Suppose now that the regulator decides whether the new product should be marketed or not using the Tullock contest (1980). Anticipating the equilibrium of the contest, the \textit{ex ante} expected social surplus will equal\footnote{The calculus can be found in the Appendix.}  \begin{alignat}  {1}  s^{*}\left(b,k\right)= \begin{align}  s^{*}\left(b,k\right)  =  & \int\nolimits _{0}^{1}\left[\pi\left(x^{\ast}\left(\delta\right),y^{*}\right)\left(b-\delta\right)-x^{\ast}\left(\delta\right)-y^{\ast}\right]d\delta\nonumber \\ = & \left(b-\frac{1}{2}\right)+\frac{\left(1-k\right)^{2}}{2\left(b-k\right)+\left(1-k\right)^{2}}\left(\frac{1}{2}-2b+k+\frac{1}{3}b^{2}f\left(\frac{k}{b}\right)\right),\label{eq:s*}  \end{alignat}  where we define for all $0\leq k/b\leq1$