I'm familiar with the PS Vita's Cross-Play games, which can carry your Vita progress over to your PS3, or vice versa.
This got me to wondering if it was possible to play any of the PS Vita Store's downloadable PSP titles with someone using a PSP, assuming the game itself has multiplayer.
For example, if I tried to play Dissidia Final Fantasy on my PS Vita against a friend who was playing it on the PSP, would I be able to do this?