> For the complete documentation index, see [llms.txt](https://dgtnetwork.gitbook.io/dgt-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://dgtnetwork.gitbook.io/dgt-docs/5.-exploring-tokenomics/5.5-token-supply-model/5.5.3-supply-protocol.md).

# 5.5.3 Supply Protocol

The modeling journey commences with establishing the **Token Supply**. As part of the simulation, the initially reserved amount of ![](/files/tpjbO3n583QLEPsDIENn) tokens is gradually distributed to the nodes participating in the maintenance of the network (Lucki\_Nodes) through the function defined in ![](/files/2lvfltica6c5BxjnWWPt)

<figure><img src="/files/gLBqWMGm8eFgkUIuDskI" alt=""><figcaption></figcaption></figure>

The subsequent step is estimating token consumption, thereby reducing any surplus. The Token Supply integrates with the profile ![](/files/qppwdpcYByfv7dGX5lD7) (reminiscent of the reward allocated to bitcoin miners) and ![](/files/pJH9HaybNx6IMOK4APL6), representing the token distribution at its zenith. The formulation is:

<figure><img src="/files/pVDqoXOSWKaqroICiVA8" alt=""><figcaption></figcaption></figure>

Here:

<figure><img src="/files/SHa4wsGy0vxNwvrDgqIr" alt=""><figcaption></figcaption></figure>

The DGT Supply Protocol ensures that early-bird nodes don't hoard a disproportionate token share. This safeguards equity and ensures that as transaction volumes, node counts, and token value escalate, the reward per node wanes.

* **Dissecting** ![](/files/fPNTqAiYOsZJh9c35IFr): Within our framework, ![](/files/UHwn8XlbtBIyQzndhC9a) prescribes the tempo of token distribution. Formulated using an inverted sigmoid function, it offers a seamless transition between stages. By analogy, while Bitcoin's rewards see periodic halving, the DEC Token (DGT) network embraces a more gradual decrement. The reward decrement adheres to this inverse sigmoid function:

<figure><img src="/files/braBO0oRjvxebP0QbsFL" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/D2w0sFLNDWFq3ZcvM1yY" alt=""><figcaption></figcaption></figure>

* **Token Distribution Dynamics**: Token distribution, within this framework, is a measured venture that strategically depletes the initial token reserve, ![](/files/oJE6FBzIQxNRCVZ8VWPT), over time. The temporal trajectory is orchestrated by parameters like ![](/files/HpX28o4rQ6mU8TPLnn3R), which contour the distribution curve and govern the token volume during each event. Here, ![](/files/zKPvb8Z4rhCX97cQ6DiG)modulates the curve's steepness, thus influencing token distribution pacing. Simultaneously, ![](/files/gJrUAQDauGQlkHr843QN)prolongs the distribution curve's span, ensuring sustainable token dispensation. ![](/files/0LxzRdqCR5PKOwtKhkBQ) then serves as a scaling factor, determining the token volume at each distribution event, thereby shaping a balanced and sustainable token economy.

<figure><img src="/files/Wayt9N4umvsauZZqUs2O" alt=""><figcaption><p><em>Figure 81 S_{PROFILE}^{SLA} over time</em></p></figcaption></figure>

<figure><img src="/files/zGWueLIqKWifR5C26QN8" alt=""><figcaption><p><em>Figure 82 Token Supply S^{SLA}\left(t\right)</em></p></figcaption></figure>
