Auto PvP is asynchronous ranked combat: you attack a snapshot of another player's team, piloted by their own autoplay settings, and they attack yours. It opens at floor 15 with ten attacks a day; standings are cut every week for pay, and nothing ever resets your rating.
Open the MENU and pick PVP ARENA. Auto PvP is the left card.
Your attacks for the day are counted on the card - ten a day, refilled at the daily reset. MATCHMAKING spends one and the server picks a defender near your power, then the fight plays like any other battle.
You attack with the party you have equipped right now. Your defense is a daily snapshot of that same party, fought by your autoplay settings - the toggle and gear on the card set how it fights - so re-gearing shows up on defense at the next reset.
Every settled match moves both ratings; the RANKINGS button opens the boards. The Auto PvP standings are cut once a week and the top ten are paid - incense and bait for the leaders, and a medal for first - if you fought at least one match that week.
Screenshots are taken from the live game by tools/tutorial_shots_b.py (dfmc-client) and regenerated after interface changes. The rules behind each screen: system-auto-pvp, system-pvp.