More info: The probability of success for the Mediator's skills is determined by Magic Attack power (MA) and Zodiac sign compatibility. Aside from 'Invite', they also have a wonderful support skill called 'Train', which automatically invites a monster when the Mediator delivers a physical attack that lowers the monster's HP to a critical level (1-15% of full HP, I think). Be careful not to kill the monster, though, or it won't 'Invite'. Be sure to 'breed' more powerful monsters once you've invited one; just walk around for several days with a monster in your party and you'll see eggs appearing in your 'Formation' screen. Happy hunting!