Your character climbs up in ranks by defeating other characters in the arena. The following is applicable for battles in the arena:
In our example character Y has a higher rank than character X.
# If character X defeats character Y, both characters exchange ranks.
# If character X loses, nothing happens.
To ensure that high ranking characters do not keep their rank by avoiding the arenas, we have introduced a quota. This means that characters have to defeat a set amount of characters each week to keep a rank.