# How It Works

### Mathematical Analysis of Revenue Sharing in Zig Network

#### 1. Introduction

Zig Network aims to implement a revenue-sharing model that distributes a portion of the network’s earnings among its participants. This section will provide a detailed mathematical analysis of how the revenue-sharing mechanism works, including formulas for calculating individual shares, total revenue, and various scenarios influencing distribution.

#### 2. Revenue Generation Model

The revenue of Zig Network can be generated from multiple sources, including but not limited to:

* **Transaction Fees (TF)**: Fees collected from each transaction processed on the blockchain.
* **Staking Rewards (SR)**: Rewards from staking mechanisms within the network.
* **Partnership Earnings (PE)**: Income from collaborations with external services or platforms.

Let’s define the total revenue (TR) generated in a given time period TTT:

TR(T)=TF(T)+SR(T)+PE(T)TR(T) = TF(T) + SR(T) + PE(T)TR(T)=TF(T)+SR(T)+PE(T)

#### 3. Revenue Sharing Mechanism

Zig Network will allocate a predetermined percentage of total revenue to be distributed among token holders. Let ppp be the percentage allocated for revenue sharing, which can be defined as:

p=RTR(T)p = \frac{R}{TR(T)}p=TR(T)R​

Where RRR is the revenue allocated for distribution. The revenue-sharing pool can be expressed as:

R=p×TR(T)R = p \times TR(T)R=p×TR(T)

#### 4. Token Holder Distribution

The distribution of revenue among token holders is based on the number of tokens they hold relative to the total number of tokens in circulation. Let:

* HiH\_iHi​ = Number of tokens held by user iii
* TtotalT\_{total}Ttotal​ = Total number of tokens in circulation

The share of user iii in the revenue-sharing pool can be calculated as:

Si=HiTtotal×RS\_i = \frac{H\_i}{T\_{total}} \times RSi​=Ttotal​Hi​​×R

#### 5. Example Calculation

**Scenario Setup**

* **Total Revenue (TR)** over a given period TTT: $1,000,000
* **Percentage allocated for revenue sharing (p)**: 20%
* **Total tokens in circulation (T\_{total})**: 10,000,000
* **Tokens held by user A (H\_A)**: 1,000,000
* **Tokens held by user B (H\_B)**: 500,000

**Step-by-Step Calculation**

1. **Calculate Total Revenue Allocated for Distribution**:

   R=0.2×1,000,000=200,000R = 0.2 \times 1,000,000 = 200,000R=0.2×1,000,000=200,000
2. **Calculate User A’s Share**:

   SA=1,000,00010,000,000×200,000=20,000S\_A = \frac{1,000,000}{10,000,000} \times 200,000 = 20,000SA​=10,000,0001,000,000​×200,000=20,000
3. **Calculate User B’s Share**:

   SB=500,00010,000,000×200,000=10,000S\_B = \frac{500,000}{10,000,000} \times 200,000 = 10,000SB​=10,000,000500,000​×200,000=10,000

#### 6. Factors Influencing Revenue Distribution

**6.1. Token Burn Mechanism**

To maintain the value of the tokens and encourage holding, Zig Network may implement a token burn mechanism. Let BBB represent the total tokens burned over a period, reducing the total supply:

Ttotal\_new=Ttotal−BT\_{total\\\_new} = T\_{total} - BTtotal\_new​=Ttotal​−B

This change affects revenue distribution since fewer tokens in circulation will result in larger individual shares for holders. The revised share for user iii becomes:

Si=HiTtotal\_new×RS\_i = \frac{H\_i}{T\_{total\\\_new}} \times RSi​=Ttotal\_new​Hi​​×R

**6.2. Growth in Revenue**

If Zig Network experiences growth in transaction volume, the revenue can increase significantly. Suppose the transaction fees grow by a factor ggg (growth rate), affecting TFTFTF:

TFnew=TFold×(1+g)TF\_{new} = TF\_{old} \times (1 + g)TFnew​=TFold​×(1+g)

The new total revenue can then be recalculated, impacting the shares distributed:

TRnew(T)=TFnew(T)+SR(T)+PE(T)TR\_{new}(T) = TF\_{new}(T) + SR(T) + PE(T)TRnew​(T)=TFnew​(T)+SR(T)+PE(T)

#### 7. Risk Assessment and Variability

**7.1. Revenue Fluctuation**

The revenue-sharing model is inherently subject to market volatility. For risk assessment, we can define a variability coefficient vvv which can affect revenue estimations:

TRest=TRbase×(1+v)TR\_{est} = TR\_{base} \times (1 + v)TRest​=TRbase​×(1+v)

Where TRbaseTR\_{base}TRbase​ is the expected baseline revenue. This variability impacts the expected shares for each user, necessitating regular adjustments based on market performance.

#### 8. Conclusion

The revenue-sharing model of Zig Network employs a mathematical framework that effectively distributes earnings among token holders based on their stake in the network. By incorporating growth factors, user participation, and a mechanism for token management, the model aims to incentivize users and ensure equitable revenue distribution. This detailed analysis demonstrates the robustness of Zig Network's approach to creating a sustainable and rewarding blockchain ecosystem.