Approximate Revenue from Finite Range Mechanisms

We consider an economic environment where a seller wants to sell an indivisible unit of good to a buyer. We show that revenue from any strategy-proof and individually rational mechanism defined on closed intervals of rich single crossing domains considered in \citep{Goswami1}, can be approximated by the revenue from a sequence of strategy-proof and individually rational mechanisms with finite range. Thus while studying optimal mechanisms without loss of generality we can study mechanisms with finite range.