The Mars One website lists SpaceX as a supplier for their launch vehicle and that they did receive a "letter of interest" from them along other suppliers. Mars One cofounder Bas Lansdorp has visited SpaceX, but they have been very quiet about their relationship with Mars One. With Elon Musk's goal of Mars colonization it appears that the two organizations do have similar interests, but is the relationship possibly competitive? Will SpaceX publicly support Mars One? If so, what milestones, if any are they waiting for from Mars One to make such a statement?
The cooperation between Mars One and SpaceX will become serious after they sign a binding contract of some sort. Until this is the case, their relationship will be very loose and will not force any party to do anything by any date. So far there is no such contract signed between the 2 parties.
Basically, SpaceX won't be doing anything, until Mars One makes an obligatory order for a launcher or some other hardware.
Mars One's schedule, budget, business idea (live TV reality show from Mars?) and some of their technical proposals are unworkable. But they have been extremely effective in marketing! They have indeed already created popular support for missions to Mars. If they focus on their (Earthbound) marketing skills, they might in that respect very well become a part of real Mars missions designed and financed by others. SpaceX (and even NASA) could gain by cooperating with them.
Mars One has said multiple times that they have no intent of building their own launch hardware; as such, there's no way they could be "competitors" to SpaceX... at least, not directly.