Reputation tokenomics

Here we analyze the tokenomics derived from the REP Token Minting Mechanism. That means we detail models for REP token evolution under a variety of assumptions, such as when the DAO enjoys constant or exponentially changing rates of incoming fees. We derive the income stream of a REP token, and calculate its present value.

The results give us more precise intuition for how to manipulate the parameters to drive the system in different ways. For instance, a DAO may choose to change the number of tokens minted when fees enter the system (a parameter denoted by $m$). The analysis shows how inflationary minting of REP encourages decentralization, and to what degree parameter choices strengthen or weaken the effect. Such calculations precisely account for how different types of members (especially older or newer members) benefit from different DAO governance decisions, which clarifies the true moral principles the DAO embodies. This allows us to compare the functioning of a DAO against its marketing, in order to objectively evaluate the group’s values and integrity.

REP Valuation

Basic parameters

REP valuation models are based on the following parameters:

1. $R(t)=$ the total number of REP tokens in the DAO at time $t$.
2. The rate of total fees $f'={df \over dt}$ that the DAO earns. Therefore $??$ denotes the total fees earned from the beginning of the DAO until time $t$.
3. $f_{0}^{1}(t)=$ is the cumulative reputational salary collected for one token from start time $t_{0}=0$ when the token was minted until time $t$. This is our function of primary concern. After determining its formula, we are most interested in its present value .
4. $m$ is the minting ratio. This is the proportion of REP tokens that are minted relative to the fees the DAO collects. The default assumption is $m$.
5. $r$ is the base interest rate or the inflation rate of the stable coin in which the fees are paid. The default assumption is $r=4\%$.
6. $L$ is the lifetime after which a token expires. The default assumption is $L=\infty$. The token can be programmed to maintain full potency until it expires, or dwindle in power according to an attenuation function. In traditional finance, the lifetime is often referred to as its maturity, or expiration, meaning the initial length of a contract upon its inception. The tenor is the length of time remaining in the lifetime of a financial contract, $L-t$.

Fundamental results

The basic results from which all other applications can be derived are summarized in the following theorems, which give the present value of a single REP token when it is minted.

Theorem 1.  (Infinite Life Tokens) 

$$R(t)=\int _{-\infty }^{t}m*f'(s)ds=R_{0}+\int _{0}^{t}m*f'(s)ds$$

where $R_{0}=R(0)$. The reputational salary of a single token is therefore given by the income stream

$$f_{0}^{1}(t)=\int _{0}^{t}{\frac {f'(s)}{R(s)}}ds.$$

The present value at time $t_{0}=0$ when a single token is minted in a DAO is

$$PVf_{0}^{1}=\int _{0}^{\infty }e^{-rt}{\frac {d}{dt}}f_{0}^{1}(t)dt=\int _{0}^{\infty }e^{-rt}{\frac {f'(t)}{R(t)}}dt.$$

Proof.

Theorem 2. (Constant fees)  

Assume the DAO is in the market position of earning fees with a constant rate $f_{0}'$ and the lifetime of a token is infinite, $L=\infty$.

Then the reputational salary of your single REP token is

$$f_{0}^{1}(t)={\frac {1}{m}}ln{\frac {R_{0}+mtf_{0}'}{R_{0}}}$$

and the present value is

$$PVf_{0}^{1}=\int _{0}^{\infty }{\frac {f_{0}'}{R_{0}+mtf_{0}'}}e^{-rt}dt={\frac {1}{m}}exp{\biggl (}{\frac {rR_{0}}{mf_{0}'}}{\biggr )}\int _{\frac {rR_{0}}{mf_{0}'}}^{\infty }{\frac {e^{-s}}{s}}ds$$

Proof.

Theorem 3.  (Finite Life Tokens)

Assume the REP tokens have finite lifetime $L<\infty$. Then the total number of active REP tokens at any time $t$ is

$$R(t)=\int _{t-L}^{t}m*f'(s)ds.$$

Then, assuming a single token was minted at time $t_{0}=0$  the fees it earns is given by

$$f_{0}^{1}(t)=\int _{0}^{min\{t,L\}}{\frac {f'(s)}{R(s)}}ds.$$

(Constant Fees)

Now assume the rate of fees $f_{0}'$ is constant. At any time $t$ after the DAO reaches token number equilibrium $t>L$, there will always be $R(t)=R_{\infty }=mf_{0}'L$ tokens in the system. The income stream of a single token is then

$$f_{0}^{1}(t)={\begin{cases}{\frac {t}{mL}}&{\text{if }}t<L\\{\frac {1}{m}}&{\text{if }}t\geq L\end{cases}}$$

and the present value of 1 token at time $t_{0}=0$ when it is minted is

$$PVf_{0}^{1}={\frac {1}{m}}{\frac {1-e^{-rL}}{rL}}.$$

(Exponential Fees)

Now assume a DAO has exponentially growing fees $f'(t)=f_{0}'e^{ct}$ and lifetime $L<\infty$. After the DAO has been running $L$ units of time, the number of active tokens will grow at a proportional exponential rate. The income stream of a single token is then

$$f_{0}^{1}(t)={\frac {c}{m(1-e^{-cL})}}min\{t,L\}$$

with present value

$$PVf_{0}^{1}={\frac {1}{m}}{\biggl (}{\frac {1-e^{-rL}}{rL}}{\biggr )}{\biggl (}{\frac {cL}{1-e^{-cL}}}{\biggr )}$$

Proof.

Consequences

??What's all this mean?

Applications

• BONDS
  • iBONDS
  • fciBONDs
  • fREP
• REP Market
  • graceful exit
  • underwriting
  • generalized chit fund banking
• stable coins
• PoR block production consensus