What would be the fall out a scenario in which

Nintendo agrees to supply certain of their IP to PS4 (and possibly PS5). 

In return Sony agrees to support the next Nintendo handheld/Fusion device (so long as its not a direct competitor to the PS4/5) and also throws in a money hat to Nintendo (under the condition the Playstation division is profitable) and marketing support.

Nintendo also has the rights to make a PS4-Fusion hybrid platform that plays games from both (Sony gets paid for their end of the hardware of course). 

Sony/Nintendo could also work out a deal whereby perhaps Sony supplies parts for the next Nintendo handheld (LCD screen, camera, battery?). 

Nintendo gets titles like Uncharted, God Of War, Gran Turismo, etc. for their portable which is more of a bonus. But it could also trigger larger third party support for Nintendo in the handheld relam with Sony officially alligning with them in that sense. 

I think it'd be a win-win for both sides. Of course I suspect ardent loyalists on both sides won't be happy, but the game industry is changing so much, I think Nintendo especially needs to decide whether it makes sense to have to pointlessly fight all these battles. Make an ally for a change. It's good for business. 

Franchises like Mario/Mario Kart/Zelda deserve to be available to more people and this solution is better than in 4-5 years have to grovel to making cheapo smartphone games if things don't improve for Nintendo. Sony's game division is good people, Yoshida and Hirai get it. 

Sony are likely the only console player that can sell over 100m now. Nintendo need sony more than sony need nintendo. I doubt it would ever happen but I'd welcome it.

On my opinion, Nintendo and Sony Computer Entertainment will merge anyway sooner or later. The shrinking Japanese market is just not big enough for two console makers.

There is no way Sony can make all their first party games for a Nintendo handheld and still provide a healthy stream of first party games for their console that rivals Microsoft's exclusives.

Also if Nintendo's handheld plays all PS4 or PS5 games, and it will no doubt be cheaper, how is that not a competitor for the PS4 or PS5?

Even if Sony is going to get rid of their handheld and Nintendo of their console, do you really think there is a possibility of such a thing happening?
I am pretty sure Sony wouldn't care at all and Nintendo would just go handheld only in that case.
I don't see games like Uncharted and God of War selling well on a handheld anyway, so that would probably profit the PS5 much more than the "HDS".

You act as if Sony can't survive with the rest of the world's sales.

No thanks... Nintendo IPs on Sony platform would Benefit Sony a lot more than Sony IPs on Nintendo platform and Nintendo can make their own hardware as long as they get over their "we must include a gimmick" aspect so Sony providing their own hardware to Nintendo wouldn't benefit Nintendo's handheld very much, specially proven by the vita. And Nintendo already has the big IPs like Monster Hunter, Pokemon, Yokai Watch and others to make their handheld a success, they don't need vita's library

Exactly what I am thinking. Nintendo IPs on Sony hardware would mean that microsoft gets instantly destroyed.

Sony would need to throw a lot of money at Nintendo for this to happen.

It would play PS4/PS5 games (other than maybe via streaming, but you need to own a PS4 for that anyway). 

Sony could just set aside one division to port maybe PS3 titles to the HDS, HDS is not going to be on par with a PS4, that's just possible for a handheld (won't be a for while) and perhaps some Nintendo divisions could even work on portable versions of Sony IP (ie: Retro Studios making a God of War game).

I'm sure between the two of these giants they could finance a studio or two to make portable versions of some of these IP. 

Ekkk, This sounds horrible :p

Nintendo doesn't need Sony and vise versa.

If this was to happen (which would make zero sense for both Would only benefit sony), Sony would benefit more then Ninetndo. Western third parties parties are not making games for any handheld and thats not gonna change unless sony releases a phone hybrid and even then it will just get ports. Japanese 3rd party devs are already behind Nintendo, so little to be gained from sony contributing towards their handheld. What will sony other which other vendors can't? At the current state of business Nintendo is better off using samsung etc

Mario, Zelda etc being on PS4 would make it impossible for Microsoft to compete in any market. PS4 would outsell it 4:1.  But why would Nintendo do that if they have chance at producing a successful homeconsole, making money off the hardware and then recouping all software venue without paying sony a license fee.