If I were u I would get a xbee tranciver module and connect one to the serial port on your psp and the other to the arduino. There is plenty of documentation on how to wire a xbee with arduino and ttl signals. Second u can get a Bluetooth ttl module for like 6 bucks and if u have a android phone u can code up a costom app to work with the serial. The other way you can do it is by somehow implementing a irda in ur arduino to have communication both ways ,if u have a old psp. But what I see might be the biggest problem is the psp app coding. I'm not quite familiar, but I don't think it's easy as the arduino IDE.
Da old psp had a irda port. The serial is connected to the psp remote. They run at a ttl level.
Or the last option is to get a Bluetooth Pair of master/slave board. Which is issentialy one board connecting to another but they can tx and rx. They run about 18 bucks but they are reusable.
Good lick on ur project men. Tell me on what you decide. XD