5.6.2 Transaction-Based Token Demand

To properly assess the token demand within a network, it's important to consider various aspects of network activity. This is because different factors can drive the demand for tokens in different ways. The proposed model thus considers two main aspects: users and value transferred, each of which captures different dynamics of the network's operation.

• User-Based Demand: The approach utilized in this user-based model revolves around the notion that as the average number of transactions per user increases, so will the demand for tokens. This model introduces the concept of a dynamic demand for tokens based on user activity rather than a fixed per-user demand, which is a much more accurate representation of a growing and evolving network. In the modeling process, a sigmoid function is employed to represent the range of alterations in the demand for tokens needed to facilitate a certain number of transactions. Like previous models, the focus is on defining the shape of the function within given limits. These limits are obtained from abstract external sources, such as the analysis of existing cases.

  The token demand per user, in this context, is modeled based on the average number of transactions per user. It is important to note that this model potentially overestimates the token demand, as it aligns with the overall trend of an increasing average number of transactions per active user over time. As the network evolves and user engagement grows, more transactions are likely to occur. This model captures this trend within the set range, providing an upper limit for the token demand per user.

  The mathematical model used to describe user-based demand is:

$$D_{user\_based}^T = D_0^T + \frac{D_{max}^T - D_0^T} {1 + e^{-k_{DTUser} * (TX_{avg} - b_{DTUser})}} \ \ \ \ \ \ \ \ \tag{34}$$

Where:

o and represent the initial and maximum token requirements per user, respectively. These are defined based on prior knowledge about the network or assumptions about user behavior.

o is the rate of growth of token requirement per user as the number of transactions increases. It determines how rapidly the token demand changes with the change in transactions per user.

o is a corrective factor that can adjust the transition point in the sigmoid function.

o is average transaction number per user

Figure 86 Token Requirement per User over time (User-Based Model)

The User-Based Model for token demand, as with any model, does have some limitations. Here are a few of them:

o Simplified Representation: The model operates under the assumption that all users behave similarly and contribute equally to token demand. This simplification overlooks the possibility of variability in user behavior, with some users potentially requiring significantly more or fewer tokens than the average user.

o Overestimation: The model tends to overestimate the token demand, particularly in scenarios where network efficiency increases and the average number of transactions per user grows. This can result in an overly conservative estimation of token requirements.

o Assumption of Constant Engagement: The model assumes that the level of user engagement remains constant over time. In reality, user engagement can fluctuate due to factors such as changing user interests, competition, and shifts in market conditions.

o Exclusion of Inactive Users: While the model focuses on active users, it excludes inactive or less active users from consideration. These users, despite their lower activity levels, may still require tokens for occasional transactions, which this model does not account for.

• Value-Based Token-Demand Model: The Value-Based Token Demand Model considers the value transferred within the network, often associated with the information entropy of the system. The greater the entropy (or the more complex the information pattern), the greater the value being transferred, and thus, the greater the token demand. As per Metcalfe's law, the value of a network is proportional to the square of the number of connected users in the system. The entropy of the system, being reflective of the network's complexity, is then equated to this network value.

  The value-based token demand per user is then calculated based on this entropy. However, to bring this in line with the reality of token requirements in a system, the demand is also associated with the inverse of entropy, considering that higher efficiency (more connections, higher entropy) could lead to lower token requirements:

$$D_{value\_based}^T= A_{network} \cdot N_{MAU} \ \ \ \ \ \ \ \ \tag{35}$$

Where:

o - Network Value Factor, serves as an attempt to quantify the network's value with respect to its complexity and the number of its active participant

o is the amount of monthly active users (as part of all users).

o is the coefficient of efficiency of the network in the transfer of value (viscosity), traditionally low for decentralized networks.

Figure 87 Normalized DT value-based over time

• Whole Transaction-based Demand Model: The fusion of two distinct token demand models - the User-Based Model and the Value Transferred Model - delivers a comprehensive estimation of token demand, which is driven by network transactions. This combined model captures both the demand driven by the number of active users (MAU) and the value transfer within the network (inferred from entropy as a measure of complexity or randomness).

  In the User-Based Model, the demand for tokens increases with the average number of transactions per active user. This model essentially mirrors User Engagement, capturing the notion that as more users engage with the network, they would require more tokens to support their activities.

  On the other hand, the Value Transferred Model, anchored in Metcalfe's Law and entropy, represents the network's complexity and the value transfer that happens within it. This model suggests that as the network's complexity increases (higher entropy) and more value is transferred (more transactions), there is a higher demand for tokens.

  By blending these two models, we can better reflect the intricate dynamics of token demand in the network. The aggregate token demand, therefore, arises from both user engagement (transaction frequency per user) and the complexity of value transfer in the network:

$$D_{TX}^T= α ⋅ D_{user\_based}^T ⋅ N_{MAU} +(1-α) ⋅ D_{value\_based}^T ⋅ N_{MAU} \ \ \ \ \ \ \ \ \tag{36}$$

The DT Network represents the total demand for tokens in the network at a given time, accounting for both the demand due to network nodes and the demand due to transactions:

$$D_{Network}^T = D_{nodes}^T + D_{tx}^T \ \ \ \ \ \ \ \ \tag{37}$$

· It serves to quantify the token requirement dictated purely by operational costs. This includes the resources needed to uphold the network's infrastructure, characterized by the component, and the resources demanded by the active users and value transfer dynamics, as denoted by the component.

· This measure deliberately excludes any influence from speculative activity, i.e., token trading based on price speculation rather than operational necessity. By doing so, the value presents a clearer picture of the genuine functional demand for tokens within the network.

· Additionally, omits the contribution from staking. Staking is the act of setting aside a reserve pool of tokens to support network security, operations, and applications, which can substantially contribute to the Total Value Locked (TVL) in a network. By excluding the staking component, maintains its focus on the transactional and operational aspects of the network.

Figure 88 Token Demand over time