Mortal Kombat vs. DC Universe (MKvDCU) is a 2008 crossover fighting game developed by Midway (NetherRealm Studios involvement for MK elements) and published for multiple platforms; a PSP version was released alongside console editions. The PSP port is a handheld adaptation with distinct technical and content differences from PS3/Xbox 360 versions.

For a look at how fans have kept the crossover alive on handheld hardware:

The PSP utilized Ad-Hoc Wi-Fi for local multiplayer. This allowed two players with PSPs to fight each other, which was a significant technical achievement for a 3D fighting game on a handheld at the time.

If you are looking for high-quality, official fighting games available on the PlayStation Portable that provide a similar vibe:

The absolute best native Mortal Kombat game on PSP, featuring the full roster plus exclusive characters like Shao Kahn and Goro.