## Notes on simple tokenomics for a PoS utility token

Source: https://www.cs.huji.ac.il/~noam/pages/Tokenomics.pdf

### Basics

1. **Sybil-resistance:**
- proof of work
- proof of humanity
- proof of stake
- Stake serves as a collateral for his proper operation in the system
- Get rewarded for work
- Rewards come from user fees or
- newly minted tokens/inflation
- An alternative reward: possibility to extract some from the network (MEV)
- The above can be combined


- Adjusted reward means the “real” rewards, after taking token inflation (minting) into account. For tokens with net minting the adjusted reward is lower than the reward, while for tokens with net burning, it is higher.

2. **Token types:**
- payment tokens: Payment tokens are meant to serve as “money” typically in the sense of being a medium of exchange and a store of value.
- security tokens: Security tokens are financial instruments that provide their holders with certain legal rights or claims against an issuer
- **utility tokens:** Utility tokens can be used to automatically get some service from the platform, allowing a user to obtain some utility from it.

The research mainly deal with utility tokens: Having a token turns out to be a key ingredient in enabling the required trustless collaboration and the token’s purpose and hence its tokenomics should serve the goal of providing utility as well.

- The analysis will be appropriate when most of the value of the token, or at least a significant part of it, is derived from its utility-token aspect.

## Micro-Tokenomics: Fees and Social Welfare

This section focuses on tx fees.

**Main argument:** the optimal transaction fee is the marginal cost that the platform incurs for
running the transaction, including congestion costs if there is congestion.

- **Maximizing social welfare:** the goal of the platform is to maximize the total value that the platform brings to “the world”

**What should the platform optimize for?**

- Due to the network effects that are the inherent drivers of any Web3 system, the most important factor for a platform would be growth. A platform that grows more will survive and not only bring more “social welfare” to its whole ecosystem but also to creators and token holders. The main way one gets growth is by making sure that the platform indeed supplies as much utility as possible. Not only will this attract users to the platform due to the direct value that they get, but also “optimizing for the users” provides a better public message that is important in the Web3 community.
- **Utility ⇒ Users ⇒ Growth ⇒ Maximal value**
- The working goal of a Web3 platform with a utility token should be to **maximize the
social welfare** that it delivers.

**How Can We Maximize Social Welfare?**

Main question: which transactions should be serviced by the platform?

There are reasons why we should not service a transaction:

1. the costs (effort and resources) associated with serving the transaction are higher than the value that it gives to the user
2. the platform may likely have some limits on its capacity, and if there is more demand for
transactions than it can supply, it will have to choose the most “valuable” ones and ignore the others

**The Basic Economic Model:**

Maximizing social welfare means choosing that set of S of serviced transactions that maximizes
∑i∈S (vi-ci) over all possible sets of transactions that fit within the capacity of the platform.

- **Optimization problem:**
- Maximize ∑i∈S (Vi-Ci)
- where Vi is the user value of a transaction, and Ci is the marginal cost of the platform to service the transaction.

In order to optimize social welfare, transaction fees should be set to their marginal
costs. This aligns the user’s net utility with social welfare.

If there are more transactions to be serviced than the capacity of the platform (congestion), than the fee for a transaction should take into account not only the direct cost Ci of the transaction but also the “congestion costs”: the net loss of social welfare that it caused to the other users.

- **Constraint:**
- ∑i∈S Si ≤ K
- where K is the capacity of total resource (e.g. gas) and Si is the set of transactions serviced
- **Greedy approximation algorithm:** sort the transactions according to the decreasing value of Vi/Ci and service transactions from the top until a point where taking the next transaction will exceed the capacity limits (or until Vi<Ci).

**The concrete transaction fee mechanisms:**

Important question: do operators have some leeway to act in their behavior in the sense that other operators cannot “catch” them acting not per the prescribed rules.

- No leeway: simple block reward is enough
- If leeway exists: the operators need to be incentivized to act as desired.
1. **Pay your bid mechanism:**

Users make bids for their transactions, and the chosen operator can accept any subset that he desires of these bids – within some given capacity – and charge the bid for any accepted transaction.

- in an equilibrium we expect the fees to be equal to the marginal costs, and social welfare to be maximized.
2. **Equilibrium in the gas model:**

An operator that is paid the bids Bi will accept the set of bids S that maximizes ∑i∈S Bi.

We expect the bidding dynamics to allow bidders to find and bid (in the long term, approximately) the lowest value of bi that will make their transaction be accepted.

The equilibrium reached under this assumption will have bidders whose value per size, Bi/Si, is high enough bidding at the “equilibrium gas price” p*. However in case of low demand the bids may go below the “equilibrium gas price”.

- **Minimum gas price to be defined:** To handle this the system must mandate a minimum gas price p*≥α as part of the protocol
3. **Incentive-compatible mechanisms:**

Transparent bidding processes, like EIP-1559, can make the bidding process transparent and thus lead to equilibrium.

- As a first approximation, the EIP-1599 protocol dynamically finds a posted price for gas that well approximates the next block’s marginal congestion costs.
4. **Extracting value from users (MEV):**

Mechanisms should minimize the possibilities for such extraction, even though it may sometimes be impossible to eliminate them completely.

**Bottom line:**

Web3 systems with a utility token should aim to maximize social welfare (aka value added) that they offer. This will happen when the fees charged are equal to the marginal costs of the transactions served (including congestion costs).

## Macro-Tokenomics: Staking Costs and New Minting

- **Main argument:** staking rewards should cover the capital costs of stakers (fixed costs), should best be paid from new minting, and should be the main factor determining the minting rate.

**Frequent issue in blockchain:** the problem of running a deficit when charging only marginal costs
manifests itself whenever the marginal costs are smaller than the average costs,

- Let’s take an example: a case where the cost for serving N transactions is given $100+N*$1, where 100 is the fixed cost and 1 is the marginal cost. 10 transactions would be an average of $11, but if charging the marginal cost it is only $1 per transaction.

In a tokenized platform it is possible **to pay for the fixed costs from minting new tokens.**

- the **advantage**: keeping the fees at the level of marginal costs.
- **who pays for the fixed costs?** The aggregate of all token holders

How justified or desirable is it to put this burden on the token holders? We argue that this is the **least-bad alternative:**

- **allows** us to charge the users only marginal costs hence **maximizing use of the system**
- maximized system use will **increase the value of the token**, thus **compensating for the inflation.**

This is currently more or less the norm in existing blockchains: new tokens are minted to pay for “block rewards” that reward miners, stakers, operators (and cover fixed costs), and tx fees are an extra.

**How long is it sustainable?** Different approaches:

1. Could be sustainable for a long time, like the economic growth in the real-world
2. Growth outpaces supply, thus congestion fees will cover the fixed costs
3. Fixed costs become small as the platform grows, thus after a while it can be added to tx fees.
4. After a while fees are increased to include fixed costs, like often in the real world

**Staking costs:**

The most significant fixed costs in proof of stake systems are often the financial costs (opportunity costs) of staking,

- if the total stake is S (measured, say, in US$), and the stakers get an annual return of r%, then the **total annual cost of staking is r%*S**
- **Ethereum’s fixed cost** (Aug 2023): $42B staked, $2B reward @5% per year, 400M txs per year ⇒ $5 per transaction is the operating cost of Ethereum.

**Minting staking rewards:**

- only mint as much as is required since new minting is a burden on token holders
- the main factor that should determine the minting rate is rewarding operators for their capital costs.

**Classic PoS blockchains**

The **leader** must be **significantly compensated** for his effort in building the block, and

- **all other operators** must be **compensated for continuously “stayin’ alive”**.
- In practice:
- the transaction fee mechanism, that motivates the inclusion of the right transactions using the correct marginal-costs pricing, takes the leader’s incentives into account as well.
- Beyond these incentives we only need to compensate the leader for his fixed costs, which large enough fixed “block rewards” will do.

**New minting:**

!!!A platform must provide sufficient staking rewards to its operators, or otherwise operators will
not agree to participate in operating the platform.!!!

**Main equation:**

**(New minting in %/year) = (Staking Rewards in %/year) * (Staking Rate)**

Nominal view:

the annualized rate of new minting = R*N/S

where

- R is the total reward of per block
- S is the total existing number of tokens
- and N is the # of blocks per year

Adjusted view:

(adjusted reward rate)=(minting rate)/(staking rate)-(minting rate).

**Staking as Security:**

By definition, the security of a proof-of-stake platform relies on possession of tokens being the
means to sybil-proofness.

1. **honest majority argument:** we do not expect any malicious party to have sufficient resources to control a majority of the stake and non-malicious stakers will follow the protocol faithfully
2. **game-theoretic/economic argument:** any set of parties that together own a large fraction of the tokens will lose a lot if the platform ceases to function faithfully since it is likely that in such circumstances the token value will drop significantly.

Achieving reasonable security in face of malicious players requires staking by at least some constant
fraction of total tokens. **The fraction of tokens staked is a proxy for the security obtained.**

- staking rates inthe above table are between 20-70%.

**Calculation:**

**(New minting in %/year) = (Staking Rewards in %/year) * (Staking Rate)**

- Given **a desired level of security, and an estimate of the current rewards demanded** by stakers, one may calculate the required minting rate.
- Example: assume that stakers require 5% annual returns and that we desire a 50% staking rate. Then the required annual minting according to the equation is 2.5% (50%*5%).
- **Assumption**: that **the higher the staking reward** rate is, **the more stakers** decide to
stake their tokens.
- if the rate of staking is lower than the equation demands then each staker receives higher
rewards than “needed” and thus more stakers will flock to stake.
- ⇒ **Equilibrium is reached when the reward is equal to what the stakers demand.**

**Dynamic minting rate:**

A dynamic minting rate mechanism may allow finer control over the equilibrium of the staking rate and the minting rate as a function of the required staking rewards as they are observed from stakers' behavior.

- Example 1: Ethereum has defined a curve where the minting rate increases proportionally with the square root of the staking rate, hence making the reward rate decrease proportionally to the square root of the staking rate.
- Example 2: minting rates can be increased whenever staking rates are below the required level (and decreased when staking rates are higher than deemed necessary).

**Bottom line:**

A proof of stake platform with a utility token should cover any fixed costs of the platform by minting new tokens. The platform’s security depends on the rate of staking, the protocol should mint sufficiently many new tokens for achieving the desired security.