Looks like maybe the nomads cap might be Warp IIga. Unless those other party members choose to go a certain place, but i would guess they all went to their home point, which would imply Warp IIga, or maybe just called Warp III.

It's the Nomad's Cap... But where's the Moogle's Cap? Weren't there two items (Nomad's and Moogles's Cap) that did the exact same thing? If you get the Nomad's from here, then where do you get the Moogle's Cap? I hope you don't get it from the Fan Fest, 'cause I just don't go to stuff like that for multiple reasons.