Fat Princess on PSP? No—It's PS3 Exclusive. No Cross-Buy.

Fat Princess never released on PSP. It's a PlayStation 3 exclusive (2009, Titan Studios / Sony).

Why No PSP Version

• Different architecture (Cell vs MIPS).
• Online multiplayer focus (32-player) — PSP ad-hoc / infrastructure couldn't support it.
• No "Remote Play" support for this title.

Can You Play It on PSP Via Remote Play?

No. Fat Princess is not on the Remote Play compatibility list. Even if it were, 32-player chaos over 802.11b/g would be unplayable.

How to Play Fat Princess Today

• PS3 (Disc/PSN): Servers shut down 2019. Local/Ad-hoc only.
• PS4/PS5: Not backward compatible.
• PC (RPCS3 Emulator): Playable at 4K. Requires dumped disc/PSN PKG. Online via RPCN (custom server).

If you want a similar vibe on handheld: Castle Crashers (PS Vita/PSP via PSN? No—Vita only) or BattleBlock Theater (no portable). Stick to PS3 or RPCS3.