SetupBasicDefinitionsIn this article, we'll let$s$ represent a quantity of STEEM, let$t$ represent a quantity of some token (SMT), and let$p$ represent a price, such that $pt$ isSTEEM-valued (i.e. ifMYTOKENis trading at $p=0.05$ STEEM/MYTOKEN then $t=120$ MYTOKEN has a value of $pt= (0.05\ \mbox{STEEM/MYTOKEN}) \cdot (120\ \mbox{MYTOKEN}) =6\ \mbox{STEEM}$.
Suppose we have a market maker (or any economic agent) with a two-asset "portfolio" (inventory) of $s$ STEEM and $t$ tokens. If the price of tokens is$t$, then we may measure of the value of this portfolio, in units of STEEM, as$v(p, s, t) = s + pt$.
One common portfolio management policy is to require that STEEM should be some constant fraction $r$ of the portfolio, i.e. $s= r v(p, s, t)$ where$0< r <1$. We call this policy the \textit{constant portfolio ratio} or CPR policy, and the equation $s= r v(p, s, t)$ is the \textit{CPR invariant}.
A different portfolio management policy, discussed by the Bancor whitepaper, is called CRR or \textit{constant reserve ratio}. To discuss CRR, let us notate the total number of tokens in existence as$T$. The \textit{CRR invariant} is then defined as$s= r v(p, 0, T-t)$.
Notes on ConventionsWe must discuss where our convention varies from the Bancor whitepaper. Atsome times, when some user Alice interacts with the market maker, Alice will remove some tokens from her balance to getSTEEM from the market maker's balance. On the other hand, Bob may add some tokens to his balance in exchange for sending STEEM to the market maker's balance.
Bancor takes the convention that in this example, the market maker \textit{destroys} tokens in its interaction with Alice, and \textit{creates} tokens in its interaction with Bob. TheBancor convention suggests the market maker is not an ordinary actor, but needs system-level "special powers"-- specifically, the privilege to operate the token printing press --in order to function.
In this paper, we adopt the convention that the tokens sent by Alice to the market maker are not destroyed, but are instead added to the inventory (balance) of the market maker. Likewise, the tokens sent to Bob by the market maker are not created out of thin air; they already exist and are merely transferred from the inventory of the market maker to Bob. Thus, we show that the market maker is essentially an ordinary economic agent acting according to a deterministic algorithm -- it doesn't actually need "special powers"!
Setup Basic Definitions In this article, we'll let $s$ represent a quantity of STEEM, let $t$ represent a quantity of some token (SMT), and let $p$ represent a price, such that $pt$ is STEEM-valued (i.e. if MYTOKEN is trading at $p = 0.05$ STEEM / MYTOKEN then $t = 120$ MYTOKEN has a value of $pt = (0.05\ \mbox{STEEM / MYTOKEN}) \cdot (120\ \mbox{MYTOKEN}) = 6\ \mbox{STEEM}$. Suppose we have a market maker (or any economic agent) with a two-asset "portfolio" (inventory) of $s$ STEEM and $t$ tokens. If the price of tokens is $t$, then we may measure of the value of this portfolio, in units of STEEM, as $v(p, s, t) = s + pt$. One common portfolio management policy is to require that STEEM should be some constant fraction $r$ of the portfolio, i.e. $s = r v(p, s, t)$ where $0 < r < 1$. We call this policy the \textit{constant portfolio ratio} or CPR policy, and the equation $s = r v(p, s, t)$ is the \textit{CPR invariant}. A different portfolio management policy, discussed by the Bancor whitepaper, is called CRR or \textit{constant reserve ratio}. To discuss CRR, let us notate the total number of tokens in existence as $T$. The \textit{CRR invariant} is then defined as $s = r v(p, 0, T-t)$. Notes on Conventions We must discuss where our convention varies from the Bancor whitepaper. At some times, when some user Alice interacts with the market maker, Alice will remove some tokens from her balance to get STEEM from the market maker's balance. On the other hand, Bob may add some tokens to his balance in exchange for sending STEEM to the market maker's balance. Bancor takes the convention that in this example, the market maker \textit{destroys} tokens in its interaction with Alice, and \textit{creates} tokens in its interaction with Bob. The Bancor convention suggests the market maker is not an ordinary actor, but needs system-level "special powers" -- specifically, the privilege to operate the token printing press -- in order to function. In this paper, we adopt the convention that the tokens sent by Alice to the market maker are not destroyed, but are instead added to the inventory (balance) of the market maker. Likewise, the tokens sent to Bob by the market maker are not created out of thin air; they already exist and are merely transferred from the inventory of the market maker to Bob. Thus, we show that the market maker is essentially an ordinary economic agent acting according to a deterministic algorithm -- it doesn't actually need "special powers"!이 부분입니다.
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