Need for Speed: The Run was not released on PSP or PSP Go.
Platforms Released: PlayStation 3, Xbox 360, PC (Origin/Steam), Wii, 3DS, iOS.
Why not PSP Go? The Frostbite 2 engine demanded more GPU/CPU power than the PSP's hardware (333 MHz MIPS, 64 MB RAM) could deliver. The PSP Go also lacked a UMD drive, relying solely on digital PSN downloads; EA likely skipped it due to install size limits and hardware constraints.
PSP Alternatives: Need for Speed: Shift, Undercover, Most Wanted 5-1-0, Carbon: Own the City, Rivals (PSP/PS Vita) are on PSP.