In order to get the Seduction stat, Menace has to fully finish Courtesan training with Lady Okyanu. Once Menace gets this skill, your Arena option changes into Seduce Nobles option. Menace can also gather Skeleton guards from the Forest and Lake, as well as seduce various nobles. Since you do not have an Arena option, Menace cannot participate in the biweekly arena tournaments. After one of these tournaments, there's a random chance that Yamamoto will come and ask you why Menace isn't participating in the tournament. You will have to somehow persuade him, or else you will get the Failed Slave Ending.