Changes

We must show that a firm can do no better than pricing accoring to <math>F\,</math>. Pricing outside the support of <math>F\,</math> is dominanted and it will transpire that pricing in the support of <math>F\,</math> leads to constant profits through-out the support.

The expected profits of the firm pricing in <math>F\,</math> are:

<center><math>\mathbb{E}\pi(p) = (v-m)L + \frac{\phi}{n-1}\,</math></center>

Therefore the firm's profits are constant on the support and so must be a best-response. When <math>\phi = 0\,</math> it is weakly dominant to list. When <math>\phi > 0\,</math> and <math>\alpha \in (0,1)\,</math> a firm's expected profits when it doesn't list are:

<center><math>\mathbb{E}\pi(p) = (v-m)L + \frac{\phi}{n-1}\,</math></center>

Therefore the firm earns the same expected profit whether it lists or not. This leads to "Ed's observation".