Revision as of 12:00, 27 February 2023

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 (denoted by ). 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:

$R(t)=$ the total number of REP tokens in the DAO at time $t$ .
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 $t$ .
$f_{0}^{1}(t)=$ 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 .
$m$ 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 $m$ .
$r$ is the base interest rate or the inflation rate of the stable coin in which the fees are paid. The default assumption is $r=4\%$ .
$L$ 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 $t_{0}=0$ of a single token in a DAO is $PVf_{0}^{1}=\int _{0}^{\infty }e^{-rt}{\frac {d}{dt}}f_{0}^{1}(t)dt=\int _{0}^{\infty }e^{-rt}{\frac {f'(t)}{R(t)}}dt.$ (Constant fees)

Assume the DAO is in the market position of earning fees with a constant rate $??$ and the lifetime of a token is infinite, $??$ .

Then the reputational salary of your single REP token is $??$

and the present value is $??$

Theorem 2 (Finite Life Tokens)

Assume the REP tokens have finite lifetime $??$ . Then the total number of active REP tokens at any time $t$ is $??$

Then, assuming a single token was minted at time $??$ the fees it earns is given by $??$

(Constant Fees)

Now assume the rate of fees $??$ is constant. At any time $t$ after the DAO reaches token number equilibrium, there will always be $??$ tokens in the system. The income stream of a single token is then $??$

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

(Exponential Fees)

Now assume a DAO has exponentially growing fees $??$ and lifetime $??$ . After the DAO has been running $??$ units of time, the number of active tokens will grow at a proportional exponential rate $??$ . The income stream of a single token is then $??$

with present value $??$

@@ Line 1: / Line 1: @@
-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.
+Here we analyze the tokenomics derived from the [[Reputation#REP token design|REP Token Minting Mechanism]]. That means we detail models for [[Reputation|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 (denoted by ). 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.
@@ Line 8: / Line 8: @@
 REP valuation models are based on the following parameters:
-# the '''total number of REP tokens''' in     the DAO at time .
+# <math>R(t)=</math> the total number of REP tokens in the DAO at time <math>t</math>.
-# The '''rate of total fees'''      that the DAO earns. Therefore  denotes the '''total fees''' earned from     the beginning of the DAO until time .
+# The rate of total fees <math>f'={df \over dt}</math> that the DAO earns. Therefore <math>??</math> denotes the '''total fees''' earned from the beginning of the DAO until time <math>t</math>.
-# cumulative '''reputational salary'''     collected for one token from start time  when the token was minted until time . This is our function     of primary concern. After determining its formula, we are most interested     in its present value .
+# <math>f_0^1 (t)=</math> is the cumulative [[Reputation#REP salary mechanism|reputational salary]] collected for one token from start time <math>t_0=0</math> when the token was minted until time <math>t</math>. This is our function of primary concern. After determining its formula, we are most interested in its present value .
-# '''minting ratio'''. I.e., the     proportion of REP tokens that are minted relative to the fees the DAO     collects. The default assumption is .
+# <math>m</math> 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 <math>m</math>.
-# The base interest rate or     the inflation rate of the stable coin in which the fees are paid. Either     notion may be denoted with the symbol . The default     assumption is .
+# <math>r</math> is the base interest rate or the inflation rate of the stable coin in which the fees are paid. The default assumption is <math>r=4%</math>.
-# ??Probably going to drop     this or add a comment somewhere.??The proportion  of the fees that is given to the DAO to     fund the reputational salary. The default assumption is that 100% is given     to the DAO, i.e., that . The reasons why  might not be 0 follow two general causes,     but the calculations and results are equivalent.
+# <math>L</math> is the lifetime after which a token expires. The default assumption is <math>L=\infty</math>. 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,  <math>L-t</math>.
-## A proportion  of the fees may be given directly to the      worker who earned the fees. People often expect an immediate reward from work,      so we give the calculations, but making  it is a security threat to the      architecture. The more secure approach is the standard architecture,      which assumes only newly minted REP tokens are given to the worker, which      later earn the worker a reputation-based salary in fungible fiat currency.      The calculations suggest a compromise by setting a short lifetime for the      REP tokens. In that case, under equilibrium conditions, the time between      earning the fees and REP tokens and receiving the entire monetary payment      is exactly the expiration time.
-## A proportion  of the fees may be given to      supplementary DAOs, such as governance, development, oracles, etc. This may      be considered the DAO’s overhead. This is mathematically equivalent to VI.1.      It is also easy to calculate the result, since we can simply redefine the      fee  to be  and all calculations hold. However,      since this number  can itself change nonlinearly in time,      independently of how  changes, it is worth stating the results.      For instance, under different seasons of governance, such as when capital      is invested in development, then REP tokens minted at different times      will earn different fees due to differing overhead.
-# The '''lifetime'''  after which a token expires. The default assumption     is . 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, .
 === 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)
+'''Theorem 1'''  (''Infinite Life Tokens'') <math display="block">R(t)=\int_{-\infty}^{t} m*f' (s)ds=R_0+\int_{0}^t m*f' (s)ds</math> ''where <math>R_0=R(0)</math>. The reputational salary of a single token is therefore given by the income stream <math display="block">f_0^1 (t)=\int_0^t\frac{f'(s)}{R(s)}  ds.</math>The present value at time <math>t_0=0</math> of a single token in a DAO is <math display="block">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.</math>''(''Constant fees'') ''''' '''''
-''where . The reputational salary of a single token is therefore given by the income stream''
+''Assume the DAO is in the market position of earning fees with a constant rate <math>??</math> and the lifetime of a token is infinite, <math>??</math>.''
-''The present value at time  of a single token in a DAO is''
+''Then the reputational salary of your single REP token is <math>??</math>''
-(Constant fees) ''''' '''''
+''and the present value is <math>??</math>''
-''Assume the DAO is in the market position of earning fees with a constant rate  and the lifetime of a token is infinite, .''
-''Then the reputational salary of  your single REP token is''
-''and the present value is''
 '''Theorem 2'''  (Finite Life Tokens)
-''Assume the REP tokens have finite lifetime  Then the total number of active REP tokens at any time is''
+''Assume the REP tokens have finite lifetime <math>??</math>''.'' Then the total number of active REP tokens at any time <math>t</math> is <math>??</math>''
-Then, assuming a single token was minted at time  the fees it earns is given by
+Then, assuming a single token was minted at time <math>??</math> the fees it earns is given by <math>??</math>
 ''(Constant Fees)''
-''Now assume the rate of fees  is constant. At any time  after the DAO reaches token number equilibrium, there will always be  tokens in the system. The income stream of a single token is then''
+''Now assume the rate of fees <math>??</math> is constant. At any time <math>t</math> after the DAO reaches token number equilibrium, there will always be <math>??</math> tokens in the system. The income stream of a single token is then <math>??</math>''
-''and the present value of 1 token at time   when it is minted is''
+''and the present value of 1 token at time <math>t_0=0</math> when it is minted is <math>??</math>''
 '''('''Exponential Fees)
-''Now assume a DAO has exponentially growing fees and lifetime . After the DAO has been running  units of time, the number of active tokens will grow at a proportional exponential rate. The income stream of a single token is then''
+''Now assume a DAO has exponentially growing fees <math>??</math>'' ''and lifetime <math>??</math>. After the DAO has been running <math>??</math> units of time, the number of active tokens will grow at a proportional exponential rate <math>??</math>. The income stream of a single token is then <math>??</math>''
-''with present value''
+''with present value <math>??</math>''

Reputation tokenomics: Difference between revisions

Revision as of 12:00, 27 February 2023

Contents

REP Valuation

Basic parameters

Fundamental results

Applications

See Also

Navigation menu

Reputation tokenomics: Difference between revisions

Revision as of 12:00, 27 February 2023

REP Valuation

Basic parameters

Fundamental results

Applications

See Also

Navigation menu

Search