# Tokenomics

### Definition

Ink Coin: INK, the native token of Pendora.

### INK distribution

INK has an unlimited supply. The value of INK is paritially backed by the reserve token xDAI.

The distribution and vesting schedule

INK Coin initially issued 100 million，and will allocate as follow:

| Percentage | Purpose of Use |
| ---------- | -------------- |
| 15         | Operation      |
| 70         | DAO            |
| 15         | Investors      |

### Incentive Principles

Ink is design to encourages users to select and support good opinions.

We believe that good opinions will win out in the long-term competition of different opinions. Centain opinion is good if this opinion is consistent with future long-term public opinion.&#x20;

One's opinion must be staked with real interests, and the opinion that wins the competition should be rewarded.

To give a example: assuming there are two answers $$A\_1$$ and $$A\_2$$ for a question. A user stakes a small amount of tokens on $$A\_1$$. Currently the ratio of tokens bet on $$A\_1$$ and $$A\_2$$ is 60%: 40%. If the ratio changes to  70%: 30% ,which means $$A\_1$$becomes more popular, then this user would get more tokens than he paid before; or, the ratio changes to 50%:50%, the user would lose tokens.

### Design

#### Notations

Let $$\mathbb{N}$$ be set of natural numbers.

Let Q be a open topic(question), under which there are a sequence of responses(answers) $$A\_0, A\_1, A\_2, A\_3...$$. Different response represent different opinions.

Any user can vote for any opinion by staking tokens on the opinion. If this opinion becomes more popular, this user will get reward.

We use a random number generator to determine an unpredictable sequence of moments $${t\_n| n \in \mathbb{N}}$$, in which each moment is allocation and settlement moment of this staking pool. Let be $$T\_j$$ the period between moments $$t\_{j-1}$$ and $$t\_j$$.

Let $$a(i, j)$$ be the total stake amount of $$A\_i$$ in period $$T\_j$$, and the total stake amount of $$Q$$  in $$T\_j$$ be$$A(j) = \sum\_{i\in \mathbb{N}} a(i,j)$$. Note the proportion of $$a(i, j)$$ in $$A(j)$$ as $$p(i, j) = a(i, j)/A(j)$$.

#### Return on capital

Conside a certain period $$T\_m$$,&#x20;

* All the stake in $$A(m)$$, will be put in a stake pool.
* At the moment $$t\_{m+1}$$, the $$A(m)$$ will be reallocate to all $$A\_i$$ in $$T\_m$$, according to the ratio $$p(i, m+1)$$ in $$T\_{m+1}$$.

So the reward of capital of $$a(i, j)$$ is $$A(m)\*p(i, j+1)$$, the rate of return on capital  of $$a(i, j)$$ is decided by following equation:&#x20;

$$
r(i, j) = \frac{A(m)\*p(i, j+1)} {a(i, j)}= \frac{ p(i, j+1) } {p(i, j)}
$$

We can see $$r(i, j)>1$$ if and only if proportion of $$A\_i$$ goes up, and $$r(i, j)<1$$ is it goes down.

#### Edge case and fees

(TODO...)

#### malicious

(TODO...)
