How about they don't make one. Focus their efforts on PS4, PS Now, and VR tech. Handheld gaming is dying there really isn't room for two competitors anymore.

Aren't you contradicting yourself???

1)you are talking about experia/smarthphone which is/are far more expensive than handhelds(claimng this to be solution/future) but at the same time you say they had to be cheap????

2)your "hardware power not needed for handhelds" ?
a)why are people still buying stronger and stronger smartphone hardware?
b)the same arguement was used for wii-look how fast it ended

btw-mostmobiles already have more power than vita-even cheap ones.

The problems about graphics is: no matter how powerull smartphones will be there is almost no market for AAA games.

The siruation is even worser than on PC where almost no exclusiv AAA games exist because of low sales but cheap ports from consoles.

mobiles don't even have cheap console ports of AAA games.

How about no handheld at all...just tablet (or tablet range) with Google Play and PS Store and similar hardware concept as this one:

I think the Xperia Play could work if it had better implementation. The idea of a device with access to the Play Store and the PS Store sounds really appealing, but it had to be marketed as a smartphone, not a handheld console. "Wow, I can play PlayStation games on my phone!" instead of "Meh, I can play Android games on my PlayStation...?".

Pay for a lot of big titles exclusive for the handheld. Get an exclusive Monster Hunter, Final Fantasy, GTA, and Metal Gear for release shortly after launch. If you've got really big exclusives that are going to stay exclusive then people will buy it.

Don't just jump in and assume everyone is going to develop for you just because you're Sony. You've done this with the PS3, the PSP, the Vita, and even the PS4. Sony is lucky with the PS4 because devs actually do want to develop for them, but Sony is hurting themselves badly by not following Microsoft and Nintendo's examples and securing exclusives.

More variety of apps, BBC iPlayer itv player, How come I can get ps2 gta games on my phone for under £5 yet thec actual handheld console does not

Meh, the days of exclusive third-parties are over. Not even FF, KH or MGS are exclusive anymore. PS3 didn't secure anything (and the 360 had Bioshock a whole year before, not to mention Mass Effect) and it turned out pretty well. Nowadays, the decising factor are the first-parties, and Sony is in a better position than MS in that regard, imo.

Also, I don't know in what universe is Nintendo securing exclusives.

I don't think they will make another dedicated handheld. Sony's handheld gaming will more than likely be integrated with whatever tablets they have and the Xperia. I think this is where PS Now comes in.

okay i got a great idea. this is what they should make next.

The hardware of the Vita is not the problem, so why change it?

If adding compatibility for Android-games is the solution, it could be easily done on the same hardware. A Cortex-A9 SoC is very common on Android devices: http://en.wikipedia.org/wiki/ARM_Cortex-A9_MPCore