Changes

<center><math>\alpha = 1 - \left ( \frac{\frac{n-1}{n-1}\phi}{(v-m)S} \right )^{\frac{1}{n-1}}\,</math></center>  This is obtained by equating the inside and outside options and solving for ><math>\alpha\,</math>.  The outside option is: <math>(v-m)\left(L-\frac{S}{n}(1-\alpha)^{n-1}\right)\,</math>, where <math>(v-m)\,</math> is the mark-up, <math>\frac{S}{n}\,</math> is the traffic if no-one else lists and <math>(1-\alpha)^{n-1}\,</math> is the probability that no-one else lists.  The inside option is: <math>(v-m)\left(L - S(1-\alpha)^{n-1}\right)-\phi\,</math>, where <math>S\,</math> is the traffic obtained from listing and <math>\phi\,</math> is the cost of listing.