i do own a psp. i must say... everytime i buy a game, i would always ask if monster rancher is going to come out but is always disappointed.
im really upset that there is no monster rancher for the PSP series. I really did have fun playing monster rancher 2 on the playstation and monster rancher 3 on the ps2.
my fondest memories was MR2... i was just hooked onto it and everything back then seemed so happy. sigh!
It is possible to play this game in your PSP. What you need is to let your PSP be able to read download-form games (like ISO/CSO/etc.) - they called it popsloader/custom firmware of a certain version. Just go to www.pspiso.com to look about the popsloader (emulator) and the download-form of the game (eboot.pbp + bin.file).
And it is technically illegal to play them as such. Don't do that method. Also, you run the risk of bricking (breaking) your PSP when the next official update is released. Sony tries to prevent piracy in any form. I would love to see a Monster Rancher PSP. It seems Sony is the only company that thought about disc swapping. As their consoles are the only ones that don't reset or take you to the main menu when you eject a disc.