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**Authors**: Alfonso Cevallos, Fatemeh Shirazi (minor)
**Last updated**: 19.11.2019
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# Token Economics
Polkadot will have a native token called DOT. Its main functions are as follows:
1. Economics: Polkadot will mint or burn DOTs in order to reward the nodes that run the consensus protocol, to fund the treasury, to control the inflation rate, etc.
2. Slashing: DOTs also play a role in the slashing protocols designed to desincentivize attacks or adversarial behaviors.
3. Governance: DOTs are also used as voting power, to let DOT holders express their opinion in governance decisions via referenda.
3. Parachain allocation: Finally, DOTs are used to decide which projects are allocated a parachain slot, via auctions and deposits.
In this section we focus on the first use above, while each of the other three uses is analyzed in a separate section.
## Introduction
Polkadot is a proof-of-stake based platform where a set of validators, who have staked DOTs, produce blocks and reach consensus. If a validator steers away from the protocol, some of his DOTs are slashed, but otherwise he gets paid for their contribution (roughly) proportional to his staked DOTs. The set of nodes elected as validators changes constantly (in each era, i.e. around once a day), but the number remains limited. However, any number of DOT holders can also participate indirectly in the decision-making processes as *nominators*, in what we call *nominated proof-of-stake*. A nominator indicates which validator candidates she trusts, and puts some DOTs at stake to support her nomination. If one or more of her nominated candidates are elected as validators in an era, she shares with them any economical rewards or punishments, proportional to her stake. Being a nominator is a way of investing one's DOTs, and of helping in the security of the system. Indeed, the larger the total amount of DOTs staked by nominators and validators, the higher the system security, because an adversary needs that much more stake -- or nominators' trust -- before it gets any nodes elected as validators.
We therefore aim at having a considerable percentage of the total DOT supply be staked by validators and nominators. Another large percentage of the DOT supply will be frozen as deposits by the commercial blockchains who get a parachain slot. We originally aim to have around 50% of DOTs staked in NPoS, and 30% in parachain deposits. As a reference, the percentage staked in other PoS-based projects is as follows.
- Tezos is 65.73% staked
- DASH is 58.69% staked
- Lisk is 58.20% staked
- EOS is only 35.49% staked, but that is because it is DPoS and the yield is low.
## Organization
This note contains the following subsections.
* **NPoS payment and inflation:** We describe how we reward well-behaving validators and nominators in our nominated proof-of-stake. Since the DOT minting for this end is the main cause of inflation in the system, we also describe our inflation model here.
* **Transaction fees:** We analyse the optimal transaction fees on the relay chain to cover for costs, discourage harmful behaviors, and handle eventual peaks of activity and long inclusion times.
* **Treasury:** We discuss how and when to raise DOTs to pay for the continued maintenance of the network.
Finally, in the last paragraph of the note we provide links to additional relevant references about the Polkadot protocol.
## NPoS payments and inflation
We consider here payments to validators and nominators for their participation in the protocols of block production (BABE) and finality (GRANDPA). We consider only the payments coming from minting new tokens, in normal circumstances. In particular we do not consider slashings, rewards to misconduct reporters and fishermen, or rewards from transaction fees. These will be considered in other sections.
As these payments are the main driver of inflation in the system, we first study our inflation model.
### Inflation model
Let \(x\) be the *staking rate* in NPoS at a particular point in time, i.e. the total amount of tokens staked by nominators and validators, divided by the total token supply. \(x\) is always a value between 0 and 1.
__Adjustable parameter:__ Let \(\chi_{ideal}\) be the staking rate we would like to attain ideally in the long run. This value should probably lie between 0.3 and 0.6, and we originally set it at \(\chi_{ideal}=0.5\). If it falls, the security is compromised, so we should give strong incentives to DOT holders to stake more. If it rises, we lose liquidity, which is also undesirable, so we should decrease the incentives sharply.
Let \(i=i(x)\) be the yearly *interest rate* in NPoS; i.e., the total yearly amount of tokens minted to pay all validators and nominators for block production and Grandpa, divided by the total amount of tokens staked by them. We consider it as a function of \(x\). Intuitively, \(i(x)\) corresponds to the incentive we give people to stake. Hence, \(i(x)\) should be a monotone decreasing function of \(x\), as less incentive is needed when \(x\) increases.
* We study the yearly interest rate (instead of the interest rate per block or per epoch) for ease of comprehension. This means that \(i(x)\) is the total payout perceived by somebody that continuously stakes one DOT during a year. The interest rate per block can be easily computed from it. **(Q: do we consider compound interest in this computation? In other words, can the staked parties immediately reinvest their payment into stake?)**
* Not every staked party will be paid proportional to their stake. For instance, a validator will be paid more than a nominator with equal stake, and a validator producing a block will be temporarily paid more than a validator not producing a block. So, \(i(x)\) only works as a guide of the average interest rate.
__Adjustable parameter:__ Let \(i_{ideal}:=i(\chi_{ideal})\) be the interest rate we pay in the ideal scenario where \(x=\chi_{ideal}\). This is the interest rate we should be paying most of the time. We suggest the value \(i_{ideal}=0.2\), i.e. an ideal yearly interest rate of 20%.
Let \(I\) be the yearly *inflation rate*; i.e.
$$I=\frac{\text{token supply at end of year} - \text{token supply at begining of year}}{\text{token supply at begining of year}}.$$
The inflation rate is given by
$$I=I_{NPoS}+I_{treasury}-I_{slashing} - I_{tx-fees},$$
where $I_{NPoS}$ is the inflation caused by token minting to pay nominators and validators, $I_{treasury}$ is the inflation caused by minting for treasury, $I_{slashing}$ is the deflation caused by burning following a misconduct, and $I_{tx-fees}$ is the deflation caused by burning transaction fees.
* The rewards perceived by block producers from transaction fees (and tips) do not come from minting, but from tx senders. Similarly, the rewards perceived by reporters and fishermen for detecting a misconduct do not come from minting but from the slashed party. This is why these terms do not appear in the formula above.
$I_{NPoS}$ should be by far the largest of these amounts, and thus the main driver of overall inflation. Notice that by channelling all of the tokens destined to burning -due to both slashing and transaction fees- into treasury, we decrease the other terms in the formula (see the section on treasury). If we consider $I_{NPoS}$ as a function of the staking rate $x$, then clearly the relation between $I_{NPoS}(x)$ and $i(x)$ is given by
$$I_{NPoS}(x)=x\cdot i(x).$$
From our previous analysis, we can see that $I_{NPoS}(\chi_{ideal})=\chi_{ideal}\cdot i_{ideal}$. Since we want to steer the market toward a staking rate of $x=\chi_{ideal}$, it makes sense that the inflation rate **$I_{NPoS}(x)$ should be maximal at this value**.
__Adjustable parameter:__ Let $I_0$ be the limit of $I_{NPoS}(x)$ as $x$ goes to zero (i.e. when neither validators nor nominators are staking any DOTs). The value of $I_0$ shoud be close to zero but not zero, because we need to make sure to always cover at least the operational costs of the validators, even if nominators get paid nothing. Hence, $I_0$ represents an estimate of the operational costs of all validators, expressed as a fraction of the total token supply. We will make sure that $I_{NPoS}(x)$ is always above $I_0$ for all values of $x$, in particular also in the limit when $x$ goes to one.
For simplicity, we propose that the inflation function grow linearly between $x=0$ and $x=\chi_{ideal}$. On the other hand, we propose that it decay exponentially between $x=\chi_{ideal}$ and $x=1$. We choose an exponential decrease for $I_{NPoS}(x)$ because this implies an exponential decrease for $i(x)$ as well, and we want the interest rate to fall sharply beyond $\chi_{ideal}$ to avoid illiquidity, while still being able to control its rate of change, $i(x+\varepsilon)/i(x)$, when $x$ increases by a small amount $\varepsilon$. Bounding how fast the interest rate changes is important for the nominators and validators.
__Adjustable parameter:__ Define the *decay rate* $d$ so that the inflation rate decreases by at most 50% when $x$ shifts $d$ units to the right of $\chi_{ideal}$, i.e. $I_{NPoS}(\chi_{ideal} + d) \geq I_{NPoS}/2$. We suggest $d=0.05$.
From the previous discussion, we propose the following interest rate and inflation rate functions, which depend on the parameters $\chi_{ideal}$, $i_{ideal}$, $I_0$ and $d$. Let
\begin{align}
I_{NPoS}(x) &= \begin{cases}
I_0 + x\Big(i_{ideal} - \frac{I_0}{\chi_{ideal}}\Big)
&\text{for } 0s^*\) we slightly increase $c_{traffic}$, and if \(s