Grand Theft Auto IV on PSP? Never Released.

Grand Theft Auto IV was never released on PSP.

Why

• Engine (RAGE) Requirements: Streaming open world, Euphoria physics, advanced shaders, 512MB+ RAM. PSP: 333 MHz MIPS, 32/64 MB RAM, no shader hardware.
• Storage: GTA IV ~16 GB (PC/PS3/360). UMD max 1.8 GB. Impossible fit.
• Timeline: GTA IV launched April 2008. PSP was winding down; focus shifted to PS3/360/PC.

GTA Games Actually on PSP

• Grand Theft Auto: Liberty City Stories (2005) — Prequel to GTA III. Full 3D open world. UMD.
• Grand Theft Auto: Vice City Stories (2006) — Prequel to Vice City. Improved engine, swimming, empire building. UMD.
• Grand Theft Auto: Chinatown Wars (2009) — Top-down, stylized, touchscreen (DS) / button (PSP). Critically acclaimed. Digital only on PSP Go / PSN (delisted).

Best Portable GTA Today: Chinatown Wars on iOS/Android/Steam (updated), or Liberty City / Vice City Stories on PPSSPP emulator (phone/PC/Deck) — upscaled, widescreen, 60fps, save states.