If Scarlett tries to enter the Amphitheater area of the Outer City, her path will be blocked by a Guardsman who tells her that the amphitheater is only for "well-known traders", and that if Scarlett were well-known, well, he would know her.
This quest is optional; there really isn't that much of interest going on in the Amphitheater. After access has been granted, ore trader Deimos buys copper ore for twice the regular price, which can be quite profitable, and Scarlett can trade with the Trade Center Administrator or obtain a small quest from him.
Gain access to the Amphitheater area.
There are three entrances to the Amphitheater area. At the one facing the main bridge, to the northwest, there is a trader named Deimos standing around. Scarlett should speak to him and ask about access to the Amphitheater. He'll suggest that a friendly trader could vouch for her.
Scarlett can either reveal that she comes from the mountains (which is true, but could be dangerous if the wrong people heard about it) or offer him a bribe of 200 ducats. Either way, he will then vouch for Scarlett to the Guard, and she'll be allowed into the Amphitheater thereafter (at any entrance.)
Access to the Amphitheater.
- Delivery for the Doctor - Deliver a package to The Doctor in the Arsenal District. This quest is available from inside the Amphitheater.