Demon's Souls 2, now.

Microsoft does. It is on the DS because the DS isn't a direct competitor with the 360. It is the reason why Rare was doing a lot of Nintendo DS in mid 2000's.

Dark Souls 2.  Same game different name. 

great idea

Demon's Souls was much better in my opinion. Platinummed both. I wish Sony would team up with From, or if they don't want it, do it alone, I'm sure Japan Studio is more than capable enough in doing a  Demon's 2.

Dark Souls is Demon's souls spiritual successor.  

And people say Nintendo doesn't have enough variety...!

OK, so I'm going to start going through the Sony list, identifying the IPs that aren't owned by Sony. I chose to do Sony first only because it's the biggest list, might as well get it out of the way first. Note that unless I know what the series is where there's no link provided, I won't include it on this list - so IPs like "Arena" and "Deadline" may or may not be Sony owned - I don't know.

The following only covers up to G-Police, I will continue some time soon.

Not Sony:
Alundra is owned by Matrix Software - the sequel was published by Activision outside of Japan.
Aquanaut's Holiday is owned by Artdink, Sony published in the West only.
Beyond: Two Souls is almost certainly owned by Quantic Dream (as, I assume, is Heavy Rain)
Cliffhanger is based on the movie, and is thus a licensed game.
Crash Bandicoot, once again, is owned by Activision. Sony only owns rights to certain games, not the IP. Sony would not be able to release the games they own the rights to without Activision's permission, as it contains Activision IP. Just like how Diddy Kong Racing requires MS permission to release, even though it's part of a Nintendo IP - it doesn't mean that MS owns the Diddy Kong IP. And again, Spyro also is owned by Activision.
.detuned is likely to be owned by the developer, .theprodukkt, rather than by Sony, given the naming. It's also not really a game, but rather, an app.
Drakan is now owned by Warner Bros (who bought the developer prior to it becoming defunct)
Dyad is developed and published by Right Square Bracket Left Square Bracket Inc.
Everyday Shooter was a PSN title developed by Queasy Games and was also released on Windows.
Flow is owned by Thatgamecompany.
Flower also is owned by Thatgamecompany.

Debatable:
Anarchy (published by Psygnosis prior to purchase by Sony, developed by WJS Design - not sure which holds the rights)
Atomino (published by Psygnosis prior to purchase by Sony, developed by Blue Byte Software, which is now owned by Ubisoft)
Badman (Sony published in Japan, Nippon Ichi published in America, may be owned by Acquire (developer) or Sony)
Ballistix (published by Psygnosis prior to purchase by Sony, also by two other publishers, developed by Reflections, which is now owned by Ubisoft)
Beyond the Beyond (published by Sony, but developed by Camelot Software Planning)
Blood Money (published by Psygnosis prior to purchase by Sony, developed by DMA Design, now known as Rockstar North)
Cardinal Syn (published by branch of Sony, developed by now-defunct Kronos Digital Entertainment)
Coded Soul (published by Sony, developed by apparently-defunct Gaia, IP likely owned by Gaia but uncertain)
The Con (published by Sony, developed by "Think & Feel Inc")
Cytron (published by Psygnosis prior to purchase by Sony, developed by Lunatic Software)
Destruction Derby (really unclear - been published by Psygnosis, THQ, Sony, Soft Bank, Midway, and Gathering. Developed by Reflections Interactive (now owned by Ubisoft), Looking Glass Studios (now defunct), and Studio 33 (now owned by EA))
Escape Plan (published by Sony, developed by Fun Bits Interactive)
Fluid (published by Sony, developed by Opus)
Folklore (published by Sony, developed by Game Republic (now defunct) - may be Sony-owned, as GR pitched sequel idea to Sony)
Genji (published by Sony, developed by Game Republic (now defunct))

PSN/PS Store titles that are probably owned by their developer:
Dark Mist (developed by Game Republic (now defunct))
Dead Nation (developed by Housemarque)
Elefunk (developed by 8bit Games and Big Head Games - the two studios are closely related)
Feel Ski (developed by Yuke's)
Go! Puzzle (developed by Zoonami and Cohort Studios)

Other:
Deap Space - can't find any evidence that it's anything but a typo for Dead Space, which obviously isn't owned by Sony. Can anyone confirm that this game exists and is different from Dead Space?

The real fact here is that many NINTENDO Ips have been overlooked while Sony's list still have Crash games, but Crash Bandicoot is not owned anymore by Sony and why can't Mario Kart and Mario Party be distinct franchises? You're stating such a bold fact given the list itself isn't really accurate.

I will be fixing all of them in the morning. Sorry for the delay.