You'd have the material resources of three worlds to bootstrap the kind of mining effort we need for serious space industry. Technology would inevitably be shared rapidly between them, either by dissenting civilians or governments that don't agree with whatever superpowers decide to have at it between them. 18 billion population worth of scientists, engineers, and entrepreneurs, assuming an equivalent to our own social structures (which seems likely given how successful, albeit horrifying, European expansionism was) - the 'happy accidents' of innovation, such as the solid-state transistor, various materials and drugs, elements of biology, physics, etc. etc. would come much more rapidly, and there would be a quick population explosion after three world's worth of these came together and filled in any holes (and maybe some we haven't even discovered).
You'd get a lot of panic and fear-mongering. A big problem I can see is that there would be no MAD. If one country fired a nuke at the enemy of a country on another world, there's no backlash for the countries of either the first or third world, because it'd be simple enough to fire an IPBM in a trajectory that could have come from either. They could probably detect the launch by the time they were good enough at making missiles, but it'd be hard to differentiate between that and a satellite launch, sans an informant. You'd have a period of peace followed by some extremely tense situations. It seems unlikely that there would be a complete dearth of Kim Jong Ils, etc, on all three worlds.
On the other hand, space tourism would be much, much more attractive to the common person. Hearing the descriptions of the landmarks, wonders, art, food, and cultures of other worlds first-hand would be a huge incentive to pay a visit, much moreso than a barren moon and an inhospitable rust-bucket are to us. Knowing that there's probably an incredibly advanced Earth and possibly other worlds waiting out there couldn't hurt, especially if transmissions were around to prove it. Corporations would probably gain much more power, much more quickly, if the media inundation we face today is any indication. That might limit even the most powerful governments to a side-role in the space race. It's hard to say how settled-and-forgotten colonists would develop socially, especially religion-wise, but there would probably be some social instability there.
(Forum games seems like a really weird fit to me, and it's also much busier, but eh)