I've been working on developing a crypto-currency called eQualityCoin for a while now and hoped someone here might be able to help me "classify" the system in a formal mathematical sense.

The system's main feature is a simple rule for how it determines a purchaser's exchange rate. More specifically, if the purchaser's native/local currency is the "weakest" in the system then their exchange rate is 1:1. If the purchaser's native currency isn't the weakest, their rate is the inverse of the exchange rate of their currency to the weakest. This formula produces a "pre-normalized" value of eCoins. This value is then normalized by dividing the pre-normalized coin balance by the wallets weight (that is, it's ratio to the pre-normalized wallet universe as a whole). The normalization aspect allows user's who fund their wallets in different base-currencies to have an apples-to-apples view of the wallet's value.

I'm attaching a model I put together (which is basically a thought experiment) to try and study how the system behaves. In the model, the players fund new wallets with different base-currencies which are equally valued (in relative terms of purchasing power). To do this, I used The Economist's "Big Mac Index"; i.e., each player funds a wallet worth 10 Big Macs. Then, two players (using eCoins) agree to the exchange of 1 Big Mac. After the transaction occurs, the players convert their wallets back into units of their base-currency.

What I found is this- although the two players agree to the same price (in eCoins), once their wallets are converted back into their local currency, the price the players actually pay/receive is the same price of the good locally, in units of their local currency.

This leads me to believe that the system would price goods at purchasing power parity (I know this is an econ concept and not a statistical one, but I think it's helpful to get the point across).

If anyone could help point me in the right direction I'd greatly appreciate it. I'll rephrase my question:

*In the most general sense, what statistical system best represents a system like this?*

Side note: my background is in finance, not statistics, so I apologize if my description is unclear in any way. I do understand

*this*system, though, and I'm happy to answer any questions or to clarify anything further.

Thanks so much!

-Preston