The answer is simple, an Arcadian is an arbitrary unit of exchanged created by use for the purpose of expressing relative values of goods.
Lets look at this a little further. Say you wanted to buy some tiles from us, now we could tell you "Well 200 tiles trades for 4 cuttable stones, or 200 wood, etc." The list could be quite lengthy, and in the end cumbersome. The Arcadians simplify this process since we can say "200 tiles is worth 1 Arcadian". Now we can publish a table with values of all sorts of materials using the same reference of Arcadians. This table can be as long as we want, since the relationship between items in pre-determined. Very simple
How do the prices in Arcadians get set? It is based on our opinion of worth of the items relative to one another. It is in no way, shape, or form to be taken as anything more than the opinion of two people about values. While we do not offer most of the items for trade by themselves, and work almost exclusively with tiles, we do use the list as starting point in other trades, as it is reflective of how we value things.
Is there an Arcadian Scrip? Of course there is, but it is generally not distributed. This is not an attempt to create a currency for all of Egypt, it is express values for our tile trading.