Changes

The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L</math>; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.

* For models with vote buying, cut point appears in complete information but not incomplete information.