The World 

Alright, so the main location of the story is Hell City, but I'm still going to briefly go over the city where Dana and Billy start off in first. 

Szandor (Human City from the beginning)

The human city we begin in is called Szandor, it has high glass buildings, a giant tower made up of three intertwining curves, and very old complex maze-like rectangular iron structure now closed to the public (But a common spot for the local teens to sneak into) built after the revolution by the workers for fair compensation. It started out about a 10th of the size it eventually became, it wasn't intended to be this big place so the streets/roads are inconsistent in design, going from following a boxy grid-plan to curves and winds to random bridges to connect the madness. There are also several parks sprinkled throughout, one with an impressive fountain that used to be in front of a mansion but the mansion was torn down, that used to be called 'Gravenson's Park' but known more widely as 'South end' for its location relative to the other parks.

Dana and Billy are lower middle class, when their parents were still alive they lived in a small two story place with two cement steps, a grey chain-link fence, no heating and mice living in the walls, right behind a highway along the edge (Latreille St, off the 0'72). They could see the curvy tower (Saint Empusa) peaking above other buildings from their house. 

After the incident the pair abandoned their home and moved to a different section. They didn't settle in one part, but they found a few different houses with basements that were abandoned/in rough shape that they claimed for their own, using their powers to scare off any residents. They had about 3-4 different places they circulated between, something they started after their stuff got stolen from their first place. 

Hell City (Where majority of story takes place)

Hell City is where some demons live (Not all, just ones from this section of the world), but it is significantly larger then most others and has a more complex social structure. 

Its kind of like this island-type location, there's the main city, there's the outer ends which get less and less dense with life, and then there's The Sea of Pain, also known as The Poison Sea or The Dark Waters (Impossibly dark waters, waves sound like screams, bones at the bottom, not sand, sea monsters unique to the world live in it, some thrill seeking demons hunt them for sport, others are in debt and get sent to hunt them on orders)

In the beginning the City didn't used to follow this competition structure its known for now, it was actually a fairly new creation being only a few hundred years old. So there are some demons in this world who existed before it did. Basically the story goes that there was a bunch of bigger wars before and after one of them ended the winning set put this system in place and it ended up functioning as a way to distract from that since there were smaller fights to deal with that bloodlust/need for competition. 

Overtime as it developed the geography of the land reflected that as well, as of this point in the timeline relating to the story there are 7 distinct rings that encircle the city that become smaller as you get closer to the centre. Those in the most debt are usually out on the ends and those with the least are usually in the middle but there are exceptions. 

Within the rings there are also distinct differences between different areas but those are usually only discernible by the locals. 

The city isn't necessarily flat either, there's a sense of elevation between the rings heightening this sense that those in the centre are staring down at those below. In the very middle is a bigger modern palace type building that has mixes of older elements in it as well, with a ring in the middle (Colosseum gladiator type vibes) meant for challenges between the highest ranking demons. Those are considered a very big deal and a City wide event where most (If not everyone) shows up to watch. 

So here's the list of descriptions of the rings:

1. The centre, richest and most powerful demons live there. Have no debts but are usually in control of many. Those in debt to them have the most expensive looking chains (which in this context refers to any kind of jewelry) but also some of the more minimal looking, though they also differ more from demon to demon. Some characters from there are Moon and Lady Bird.

2. Demons from the second ring are still powerful but usually in a few debts, usually not more then three and usually only to those from the centre ring. Chains to demons from this area usually take the form of a common symbol/recognizable image/animal etc. Like those in debt to The Man with Scissors usually wear silver scissors as a pendent on a necklace or belt or something like that. Some characters from there are Strix, The Man with Scissors and The Tall Man. 

3. Chains are made from a mixture of things, usually goldish/bronze and very detailed. Demons from there are usually closer bonded family units who make a living through having many children and having those children collect debts from lower ranking demons for the labor. There also tends to be a bit of distrust within the families so it becomes increasingly common for parents for 3 in particular to challenge their children in order to keep them under their roof. Some characters from there are Carrion, Carcass, Marrow and Sarx.

4. Chains are usually metal and take the form of actual chains. Most of the residents were soldiers and some of them were higher ranking generals/commanders from the side of the war that lost. They were targeted first for being on the other side and most were overwhelmed with the challenges and caught off guard. Some characters from there are Plague.

5. Chains are made from metal, usually iron. Many of the demons from there are good forgers/involved in weapon making which reflects in their names (Often named after weaponry). Some demons from there are Falcata, Sarissa, Axe, Bolas.

6. Chains are made from beads (painted wood/metal/plastic), more colourful. Demons from there are usually either more artistic or perform more manual labor. A character from there is Harmonia. 

7. Those in debt to demons from 7 usually have chains made from found objects (bottle tabs, keys, scrap string, wire, that kind of thing). Those who live there usually gather things from the river to make a living off of. A character from there is Silverfish.

Not all the demons live in the rings either, some live on boats and explore The Sea of Pain, like a demon named Sea-Wolf a feared captain of her own ship. 

For further clarification, in the beginning there was a lot of competitions declared and overtime these 7 areas were carved out because of that because thats just either where they happened to live already or got pushed out to. Competitions are usually held between demons from rings that are closer together unless the challenger is looking for someone with a special skill which is why lower rings get targeted, most commonly high ranking demons from the first and second rings target ring 5 to get a personal forger and a few from 6 for live in servants/artists to decorate their homes. 

(I'm gonna stop here cause this is really long, if there's anything specific that should be added let me know)

The challenges themselves can technically be made between anyone, there just have to be terms set (What happens if either win), at least one challenger, the demon their challenging and a third demon to act as witness. The only reason random challenges aren't so common is cause of unspoken rules made as that system existed longer. 

The challenges also don't have to be a physical fight, though they often are, its also pretty common for them to be challenges of intellect, games of chance, challenges of skill, complex games with many competitors where one demon wins the debts of all the others. The kinds of challenges that are more common tend to differ from ring to ring and specific area to specific area, however fighting hand to hand is the usually the most popular and can be found in any of the rings.

Once the challenge is won the loser is forced to obey the winner for a certain period of time before they can re- challenge them and try to win back their freedom (If they choose not to fight again they will remain in the winners service). There are a variety of reasons for the challenges to occur, wrath, lust, greed and so on. 

In this story the demons take human form but have abilities/behaviours that aren't. Many of them are based off of bugs or animals like snakes, owls, wolves etc. 

There also gods of death who interact with them and mythological monsters which relates to how the challenge system works on a technical level, but this is already pretty long and that part of the world isn't something I'm going to explore too deeply in this story (Maybe another story from the same universe)