In two patents filed on July 14, 2009 and published on July 15, 2010, Sony appears to be investigating using stereoscopic technology to display different game scenes to two different players simultaneously, calling it "Stereoscopic Screen Sharing" (via Eurogamer).

The technology would operate under the same principles as stereoscopic 3D, which displays two alternating images to the left and right eyes, but requires double the framerate of a 2D picture. In this patent, Sony describes using this alternating to instead split the picture to two different players, instead of two different eyes. It is possible that the effect would be a distinct scene for each player, eliminating the need for splitscreen.

The glasses detailed in the patents are LCD shutter glasses, similar to those used already, but would include attached headphones so that two separate audio feeds could be delivered to each player. By doing so, two full experiences could be presented to different players using a single console and 3D capable display.

I don't know if this is something for this generation, however, as Sony is already having some difficulty with image quality and framerate with some 3D games. As for replacing splitscreen, each player's rendered scene would be much larger than what it would be on a splitscreen, doubling the pixels needed to display fullscreen scenes for both players. It is likely that image quality would suffer with current technology.

It is also unclear if the same issues affecting some 3D viewers would also affect viewers of this technology. In any case, I'm much more supportive of stereoscopic technology for this purpose than for 3D.