Understanding Commission Structures and Token Dynamics in a Tokenized Economy
1. Definitions and Notation
I: Investment amount in tokens made through an affiliate's referral link.
C: Commission earned by the affiliate, denominated in the invested token.
α: Commission rate (fixed at 10%, or 0.10 in the current model).
E: Total earnings of an affiliate.
Itotal: Total investment generated through an affiliate's referral link.
S: Current supply of tokens in the ecosystem (applicable for bonding curve scenarios).
P(S): Price of the token as a function of supply, defined by the project's bonding curve equation.
Affiliate Identifier (AID): Unique identifier associated with an affiliate, embedded in their referral link.
2. Commission Structure
The commission earned by an affiliate for a single investment is a linear function of the investment amount:
$$ C = \\alpha \\times I $$
Where α = 0.10 (fixed commission rate).
3. Payout Mechanism (Formalized)
The payout mechanism is modeled as a sequence of transactions executed on the Solana blockchain via a smart contract. Let Ti represent the i-th transaction within the system.
T1 (Investment): User invests I tokens through an affiliate link with identifier AID. The smart contract registers AID.
T2 (Commission Calculation): The smart contract calculates the commission C using Equation 1.
T3 (Payout): The smart contract transfers C tokens from the ICO's designated address to the affiliate's wallet associated with AID.
4. Impact on Token Dynamics
4.1 Increased Demand
Let D(x) represent the demand function for the token, where x represents factors influencing demand (e.g., marketing efforts, project fundamentals, market sentiment). The TokenAffiliates program aims to increase x through enhanced marketing, potentially leading to an increase in demand:
$$ D(x + \\Delta x) > D(x) $$
Where Δx represents the positive change in demand factors due to affiliate marketing.
4.2 Token Distribution
The commission payout mechanism contributes to token decentralization. Let NA be the number of active affiliates. The total tokens distributed through commissions are:
$$ \\sum_{i=1}^{N_A} C_i $$
Where Ci is the commission earned by the i-th affiliate. This distribution broadens token ownership beyond the initial investor base.
4.3 Bonding Curve Effects
For projects employing bonding curves, the increase in demand shifts the supply and influences the price. Let the initial supply be S. After an investment I, the new supply becomes S' = S + I.
$$ \\Delta P = P(S') - P(S) = P(S + I) - P(S) $$
The specific form of P(S) depends on the chosen bonding curve equation (e.g., linear, exponential, sigmoid).
Example (Linear Bonding Curve):
Let P(S) = k \\times S, where k is the slope of the linear curve. Then:
$$ \\Delta P = k \\times (S + I) - k \\times S = k \\times I $$
This demonstrates that for a linear bonding curve, the price increase is directly proportional to the investment amount.
Linear Bonding Curve Example
7. Conclusion
This formal mathematical model provides a robust framework for understanding and analyzing the TokenAffiliates program. By quantifying the relationships between key variables, the model enables a deeper understanding of the program's impact on token dynamics and affiliate earnings. Future research will focus on expanding the model to incorporate more complex scenarios and explore advanced features, ultimately contributing to the development of a more sophisticated and efficient Tokenized Economy.