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A4:\textbf{Limit Dominance}: There exist $\underbar \theta \in \mathbb{R}$ and $\bar \theta \in \mathbb{R}$, such that (i) $\pi(l,x)<0$ for all $l \in [0,1]$ and $x \leq \underbar \theta$;(ii) $\pi(l,x)>0$ for all $l \in [0,1]$ and $x \geq \bar\theta$.
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\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
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