Ghost Q appears in an optional battle, and challenges the protagonist's party to a game. There are three memory cards scattered about the map, and one of them contains treasure. No matter which order the memory cards are collected, the last one contains the treasure of 599 Macca, while the other 2 spawn copies of Ghost Q. The player has 2 options to go about this battle - either play along and collect the treasure, which will cause Ghost Q to leave without a fight (this option won't give the Prize Winner title bonus in Overclocked), or defeat Ghost Q and end the battle (earning the Prize Winner bonus in Overclocked).
Devil Survivor 2
"A mysterious ghost, said to be intense desire incarnate. During Japan's period of economic growth, it would appear in homes, where it would eat 25 bowls' worth of rice at every meal, thereby raising Engel's coefficient. However, it is afraid of dogs, so homeowners would always keep a dog on hand."
—Devil Survivor 2 Compendium
Ghost Q appears in an optional battle on the 3rd Day in Bugeikan Stage, before the protagonist leaves for Nagoya. He will decide to challenge the protagonist to a "one on one duel", immediately summoning demons to begin the fight. Having any other playable characters in your party on the field causes him to leave. He will also attempt to run to one of the stage exits if you defeat all the demons before him.
Defeating Ghost Q unlocks the ability to fuse him in the Cathedral of Shadows. He can only be obtained by fusing Jack Frost with Ogun.