As stated by others, you are required to have an installation copy for each platform.

This, however, needs to be clarified.
Quote Originally Posted by Ed_N_Ants View Post
However if you pay for more than a month at a time you can have another account on the profile, so technicially your paying for just the game and not the monthly service...
If you have the Standard Subscription of the game, you can have up to 8 characters per world and 40 characters per service account. You can not log in with any of those characters simultaneously, which is relevant to playing with someone in your household.