Parameters & Calculations

Core Parameters

• $\text\$Ā_{\text{\tiny staked}}$: The amount of $AUT staked by a Participant (Staker) on one of their Peers (Stakee).

• $\overline D$: The duration of the staking period as predicted by the Staker.

• $A_{j}$: The "age" of the ĀutID of the stakee (j), represented by the sum of all periods in their Peer Value ($\upsilon$) history ( $\sum T_{G_{j}}$).

• $\sum{\overline{D}}{G_{j}}$: represents the amount of segments $\overline D$ in which stakee’s Peer Value’s growth was equal to or greater than the predicted Growth.

• $EG$ is the Expected Growth of stakee’s Peer Value made by the Staker.

• $f\overline{D}{G_{j}}$: the amount of continuous segments of periods T, of the same length of D.

  • Calculated as: $f\overline{D}{G_{j}} = \frac {A_{j}}{\overline{D}{G_{j}}}$, where:

    • $\overline D_{G_{j}}$ is a “segment”: defined as a discrete series of periods in sequence - of the same extent of Staker’s prediction.

• $GL_{i}$: a coefficient representing the likelihood/difficulty of the Stakee to achieve or exceed the predicted growth (EG) of their Peer Value. Calculated as:

  • $\displaystyle GL_{i} = \frac{1}{\frac{\sum{(\overline{D}}{G{j}}\ge EG_{j})}{f\overline{D}{G{j}}}} \rightarrow GL_{i} = \frac{f\overline D_{G_{j}}}{\sum{(\overline{D}}{G{j}}\ge EG_{j})}$

  • or again, in prettier form:

  • $\displaystyle GL_{i} = f\overline D_{G_{j}} \times (\sum_{\tiny \overline{D} G_{j} \ge EG_{j}} EG)^{-1}$

Gains —> $\$Ā_{\tiny \oplus}$

$\$Ā_{\oplus} = \begin{cases} \$Ā_{(staked)} \times 1.5 &\text{if } \sum{(\overline{D}}{G{j}}\ge EG_{j}) = 0 \\ \$Ā_{(staked)} \times (1 + GL_{i} + \frac {D}{A}) &\text{in all other cases } \end{cases}$

where:

• $\$Ā_{\tiny \oplus}$ is the reward in $AUT to be given if the stake is successful.

Losses —> $\$Ā_{\tiny \ominus}$

$\$Ā_{\ominus} = \begin{cases} \$Ā_{(staked)} \times 0.75 &\text{if } \sum{(\overline{D}}{G{j}}\ge EG_{j}) = 0 \\ \$Ā_{(staked)} \times [1 - (GL_{i} + \frac {D}{A})] &\text{in all other cases } \end{cases}$

where:

• $\$Ā_{\ominus}$ = $AUT losses