Changes

If all users register with I, then an i user will only multihome if <math>p_i^E < 0\,</math> (as otherwise he would face a loss), and get a subsidy. If only one type of users register with E then he will face a loss (because of the subsidy pricing) as he won't be able to recoup on the transaction fees.

There is some price pair <math>(P^I, P^E)\,</math> such that with <math>n_j^I=1\,</math> and <math>n_i^M=1\,</math> that is an equilibrium if:

:<math>r_j^E < \max \{r_j^I; \lambda(1-\lambda)u_j + \lambda^2 u_j \max \{t^I,t^E \} \}\,</math>

If this (and <math>p_i^E < 0\,</math>) holds then all users will register with E, whether or not they still register with I depends on E's pricing strategy:

#Become a first source: <math>t^E < t^I\,</math>, so only users that can't match with E will perform transactions with I

#Become a sole source: At least one population must not register with I.

The profit when there is multihoming has an upper bound of <math>\underbrace{\lambda(1-\lambda) -c}_{\mbox{Multihoming Agg. Surplus}}\,</math>.

Multihoming is a market allocation if no user of type h prefers registering with I only: