Financially Sony should leave, but they won't. Not until the company completely dissolves.

MS and Nintendo won't be leaving after next gen either. I just don't see why they would.

Playstation is probably one of the few things they have left that's making money. The shitty start of PS3 and it's astronomical r&d may never be made back, but they've gotten their shit together since 09 and it's been making a profit since then. PSV is off to a slow start but it has a lot of big games lined up, Sony hasn't placed all their cards on the table and it doesn't need to be incredibly successful to make a good profit. Kaz Hirai (God among men) seems to know what he's doing, at least when it comes to playstation (as previously mentioned, the PS3 became a success right around when he started running the PS side of things at Sony)

If they're smart with PS4, it could be the most profitable thing that's come out of them in a very long time.

Nintendo will never do only SoftWare, they already said that would never happen. So if they are out, they are out.

Somebody from Nintendo saying it doesn't mean a thing. And IMO they'd be incredibly stupid to not put their IP on other platforms if their financial situation gets to the point where creating new hardware isn't worth the risk. They're IP has tremendous selling potential on other platforms, imagine how much Pokemon or Mario on IOS/Andriod would sell for example. Same applies to Sony. 

Somebody? How about Miyamoto/Reggie/Iwata saying it?

They just wouldn't it, they would drop out if they can't make their own titles for their own systems. I doubt even Sony would want to do that.

None of them. They all have reasons that they could leave/be forced out, but I don't think any of them will actually happen.

I think Sony will pull it together again with the PS4, I think Nintendo will continue to make profits even if they don't sell well, and MS... would be who I'd pick if I had to pick one. But they've got 360 momentum, tonnes of money, and Halo, I think they'll be alright.

Bad example because it's so long ago, but Sony used to release some of their titles for other systems.

Cases in point: WipEout 2097 (Sega Saturn, PC), G-Police (PC), Twisted Metal 2 (PC), Jet Moto (PC).

I agree it's probably well past that stage now, but I could see Sony as a third-party developer.  They've certainly got the studio roster for it.  Whether they'd do it anymore or simply sell off their studios is another matter.

I could totally see Nintendo or Sony as just Game Developers too but it just won't happen.

They don't, or at least Nintendo, want to have less control over their company. Making games for another would do that.

I don't think anyone will be 'eliminated' per se but I do expect next generation to be very different. Nintendo can survive off of the strength of thier properties and the fact that they sell consoles at a profit (excepting price dropped 3DSes). However, WiiU could be a repeat of the Gamecube.

MS we know is moving to a subscription model and will have a large focus on multi-media not just games. With an enhanced Kinect, I think they are the best positioned of the three to thrive next gen.

Sony we know is going after cloud. MS undoubtably is too and Nintendo would be foolish to ignore it. Cloud gaming could totally equalize the playing field, meaning all 3rd party games are playable on ALL systems, possibly even Wii (how's that for late revenge - unlikely to happen though), including 'Smart' TV's without a console at all (just controller). We know nothing of Sony's strategy otherwise (at least I don't, aside from 'power') and so I suspect Sony not Nintendo is in the weakest position going into next gen. An expensive console will fail, regardless of power. Unlike MS/Nintendo, Sony has little sway with casuals (ATM, it dominated that market with PS2) and the core is becoming increasingly less profitable to cater too. Sony sold PS2 as a DVD player, PSP as a UMD player (fail!) and PS3 as a Blu-ray player. Even the Vita requires a prepriatory memory card. There is nothing coming after Blu-ray. And how do you make digital/cloud prepriatory? I suspect Sony is going to try. And fail. But ultimately they will continue to make some of the best games around and will continue to provide a platform, even if it's only a digital one (cloud-based) on Sony 'smart' TVs and devices.

So physical consoles as we know them today may end, but I don't think Nintendo/Sony/MS position as maker/publisher/distributor of games and game playing devices will end. It will just look very different in ten years.