Reputation tokenomics

Reputation tokenomics is the economic analysis of the value of REP tokens in a DAO. Here we study the tokenomics resulting from standard DGF mechanisms for REP minting and distribution using the Validation Pool and the Forum.

The fundamental results of reputation tokenomics derive from analyzing the effects of parameter changes in the REP Token Minting Mechanism. Models for REP token evolution depend on the DAO's working parameters (such as the minting ratio $m$, the policing rate, and the lifetime of tokens) and on market factors (especially the interest rate and the amount of fees $f$ the DAO earns which determines the REP salary). The analysis follows by determining the income stream of a REP token due to this REP salary, which is equalized over time by calculating its present value.

The results of REP tokenomics help guide governance decisions. The formulas derived from tokenomics give us more precise intuition for how to manipulate the parameters to drive the system toward different goals. 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 default 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.

The formulas derived help us to rigorously program financial instruments, such as

• security tokens, e.g., BONDs
• insurance contracts
• equities, e.g., investor tokens
• ForEx instruments, e.g., stable coins
• tokenized commodities
• NFTs
• financial derivatives, e.g., calls and puts

Overview

Reputation tokenomics is a sub-discipline within general tokenomics, which is a sub-discipline of finance, which is a sub-discipline of economics. Tokenomics is the study of the value of digital tokens in online networks, originally blockchain based.

There are many valuable blockchains and DHT networks holding digital financial tokens that fall under the domain of interest for tokenomics. Currently, the digital tokens of greatest value and interest are Bitcoin, ETH, and the sub-tokens of Ethereum, typically fungible ERC-20 tokens representing ownership of DAOs and non-fungible ERC-721 tokens, called NFTs, representing ownership of individual properties.

These tokens fall under the financial instrument categories of equities, securities, commodities, utilities, and derivatives. However, most current tokens are combinations of these types. For example, the basic token of the Ethereum network, ETH, confers on its owner the power of using the network for information storage, processing, and transmission, because ETH is used to pay the network to run smart contracts. Therefore, the argument usually made to securities regulators is that ETH is a utility token. However, ETH has also been used in the past to make governance decisions. Therefore ETH also has some properties of an equity in the quasi-corporation that is the Ethereum network. ETH also has some aspects of a security, since the governance design has chosen to limit the quantity of ETH in the hopes that it will grow in value.

There is an active legal argument concerning what type of financial instruments these tokens represent for the purposes of national and international regulation. However, since Ethereum is not centrally incorporated, its governance is not structured like any traditional corporation. Therefore its regulation arguably falls outside the scope of the SEC in the US or the ESMA in Europe. (Main article: Legal regulatory issues for DAOs.) The ownership of Ethereum is certainly international and arguably supranational.

REP tokens under DGF similarly overlap these financial categories. They are utilities in that they confer the power to obtain work through the availability smart contract. They may be equities if they are the type of REP that confers power over governance in the DAO. Our primary concern in reputation tokenomics is analyzing a REP token's value as a security. REP tokens have the quality of securities in the sense that they are a type of annuity, since they hold claim over any future fees the DAO earns through the REP salary. Though REP tokens are not a typical annuity, since they pay out at random, when the DAO attracts outside fees.

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 $f(t)$ 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 REP 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 discount rate. This will be the interest rate of the economy, or depending on context, the inflation rate of the stable coin in which the fees are paid, or the CPI. 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 of REP valuation formulas

The formulas cannot directly valuate REP tokens, because a token's value is dependent on the rate of fees in the DAO in the future. However, the formulas allow us to quantitatively estimate the value of tokens by observing the past. And further, by making different assumptions about future DAO fee rates, expected present values can be predicted.

Old tokens with infinite lifetime are more valuable then new tokens

For infinite lifetime REP tokens, the present value of a REP token at minting will change depending on the rate of fees the DAO attracts. In this case, more REP accumulates as time goes on. Typically, a REP token minted earlier is more valuable than a REP token minted later, since a later token shares the REP salary with more owners of REP. One way to combat this inequity, if that is desired, is to limit the lifetime of a token.

Convergence to fair value for finite lifetime tokens

Theorem 3 shows that for finite lifetime REP tokens, the number of tokens that exist in the DAO is not important if the rate of fees stabilizes. Assuming the DAO is healthy, in the sense that it attracts a regular rate of fees, that grow with inflation $r=c$, then the present value of a token minted at equilibrium is $PVf_{0}^{1}=1/m$ which is the same amount of the fees that were brought given to the DAO in order to earn the REP token. Therefore, an expert who earned a REP token does not immediately receive the cash for their work, but they do ultimately receive more than the amount of cash they brought in. The present value of REP tokens (on average) are exactly the same as the amount of fees they attracted with their work. However, the reputation accounted for is also a signal that the owners of REP tokens have done useful work in the past, and their tokens can be slashed at any point up to time $L$.

Perfect markets

DAOs in Web3 have the potential to offer more efficient and competitive environments for business and economics. The platforms being built with P2P technology and DAO architecture are designed in line with ideal economic properties for optimizing the effectiveness of markets.

DGF allows us to create theoretically more perfect markets than legacy business environments currently provide. The following conditions are primary characteristics of an ideal perfect market. As we explain each quality, we comment on how primary DAOs designed under default DGF assumptions generally satisfy or fail to satisfy each property.

Conditions of perfect competition

• The market is deep – This means there are a large number of buyers and sellers. Primary DAOs are open, meaning anyone on the planet may participate if they follow the transparent protocols using freely available open source technology.
• Zero transaction costs – This means buyers and sellers do not incur costs in making an exchange of goods. In theory smart contracts can minimize costs to neglible amounts due to contemporary computing power. However, in practice, most existing Web3 platforms, such as Ethereum, have charged expensive fees for transactions. This is due to bad incentive design for the maintenance of previous platforms, and not an inherent property of P2P technology (e.g., Skype started as a free P2P video conferencing app that took advantage of the low cost of contemporary computing power in 2003). We use DGF to create block producer DAOs designed with balanced incentives for minimizing transaction costs to further the community's goals of profiting from authentic economic activity. Free transactions for the public can be motivated, for example, by paying nodes in REP tokens for other DAO activities which require distributed computing to achieve decentralized business.
• No barriers to entry or exit – Primary DAOs are open, which means both entry and exit can be made free of sunk costs. However, for security, some DAOs may choose to add protocols which require more or less onerous onboarding requirements for entry, participation, and exit. Graceful Exit BOND markets support barrier free exits which allow members to immediately cash out with zero threat to the governmental stability of the DAO they are leaving. DAOs which choose this option are opening an attack vector, however, since members who cash out their REP immediately in trade for BONDs cannot subsequently be slashed.
• Perfect information – This means all consumers and producers know all prices of products and utilities they would get from owning each product. This prevents subDAO firms from obtaining any asymmetric information which would give them a competitive edge. The transparency associated with DAOs leads to extremely symmetric information.
• Well-defined property rights – These determine what may be sold, as well as what rights are conferred on the buyer. In the context of a primary DAO, property rights are nearly perfectly defined by code. The major caveat is that judicial governance makes review possible.
• Rational buyers – This means buyers make all trades that increase their economic utility and make no trades that do not. In order to be decentralized and open, DAOs are required to have maximal bureaucratic transparency concerning all interactions inside and outside the group. This transparency allows more accurate audits of every business transaction, allowing free and open access to information about the market a DAO creates, so that public buyers can have maximal knowledge and understanding of market information, which encourages rational buyer behavior. Combined with openness, this gives buyers equal opportunity to make trades.
• Profit maximization of sellers – Firms sell where the most profit is generated, where marginal costs meet marginal revenue.
• Every participant is a price taker – Decentralization implies no participant has market power to set prices. Each DAO must negotiate with other DAOs for all business. However, market price negotiations requires decision making. Decision making in a DAO requires agile governance. Traditionally, decentralized organizations have a much more difficult time coming to a decision than a centralized organization, which requires only one person to decide. Thus DGF focuses primarily on making effective and efficient governance processes for DAOs.
• Homogeneous products – This means all products are perfect substitutes for each other (i.e., the qualities and characteristics of a market good or service do not vary between different suppliers). In DGF DAOs are designed to police each work contract to guarantee that it is in line with their standards using the Validation Pool.
• Anti-competitive regulation – DAOs under default DGF protocols inhibit anti-competitive activity by governance which encourages equal access to work through openness and by using availability smart contracts which choose random members for work.
• Perfect factor mobility – In the long run, factors of production are perfectly mobile, allowing free long-term adjustments to changing market conditions. This means, for example that workers may freely move between firms, which are in such supply that no monopolies exist for any sub-products. The openness of primary DAOs allows any members to join or leave at will. And DGF is a framework for creating DAOs. This means that primary DAOs, because they are by definition open source, can be cloned at will, so there is an environment which encourages strong competition. However, since the regulatory process in DGF is complete, any possible regulatory scheme is expressible with smart contracts. This means a DAO can prevent certain actions. Combined with first mover advantage and the network effect, we see that large old DAOs have some economies of scale, at least in attention. So while factor mobility in a DAO is far more perfect than any managed economy, it is not absolute.

• Non-increasing returns to scale – This means there are no economies of scale from making larger subgroups in the market, that rewards are linear. The basic design of DGF workflow ensures that REP tokens have linear powers. E.g., a member with twice as many tokens has twice as much likelihood of being chosen with an Availability smart contract, for example. No economies of scale also ensures that there will always be a sufficient number of firms in the industry. With a large enough talent pool, and with low enough transaction costs, economies of scale are eliminated. With the ability to clone open source primary DAOs which fail to provide services that are demanded, sufficient numbers of competing firms can be created to give perfect competition.
• No network effects – In economics this means that products are limited materially which allows competition to be meaningful. For example the production of shoes have no network effects, since they cannot be shared by customers and it costs the producer twice as much to make twice as many. However, radio transmission is an example of an industry with strong network effects. For example, it costs no more to transmit radio to one person within a mile of a radio station than it costs to transmit to 1000 people who live within that same mile. And the more people who use the radio station, the more valuable the service for advertising becomes, though there is no difference in cost to the radio station to produce the advertisement for one listener or for many. There is a network effect that benefits the radio station for each new listener without adding to its costs to operate. Under DGF, the typical DAO will experience many strong network effects since many products can be automated and copied. So in this regard, DAOs do not provide an environment for perfect competition, and in fact generate a great deal of free content, which we consider to be the commons of the Web3 environment, for which there is zero competition. However, assuming a DAO provides specialized work for each customer according to DGF workflow, then a primary DAO has absolutely no network effects, as proven by the fact that REP tokens are minted precisely in proportion to the fees a member earns for the DAO. In this regard, DGF provides another quality of perfect competion that makes it close to an ideal perfect market.
• No externalities – This means costs or benefits of an activity do not affect third parties. A common example illustrating the meaning of an externality in economics is pollution. When an industry pollutes, the costs are not borne by the producer nor the customer, but they are borne by larger society (the third party). This criterion prevents the need for government intervention to account for the cost to the larger society. It is difficult to identify what externalities abstract primary DAOs would have in general. However, the no externalities criterion is an ideal quality of an economic model and not a quality that is perfectly achievable in practical organizations. Therefore it is important to be continually vigilant of any externalities that any DAO may have on the economy, and take responsibility for mitigating any harm it causes. To achieve this, governance is necessary, which is why creating a framework for responsive governance is of primary concern under DGF.

An analogy that economists use for explaining the idea of perfect competition is that it is the ideal in a similar way as how physicists use the frictionless vaccuum as a basis for models of mechanics. From the analysis above, we conclude that primary DAOs generally form far more perfect markets than any legacy business environment. In fact, the current difficulty with Web3 is to create some of the inertia and friction necessary to create history.

Applications

• Treasuries
• BOND tokens
  • iBONDs
  • fciBONDs
  • fREP
• BOND Markets
  • Graceful Exit
  • Underwriting & insurance
  • generalized chit fund banking
• Stable coins
• PoR block production consensus
• REP with attenuation

See Also

• Reputation tokens
• Validation Pool