Āut Labs
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  • The $AUT Token
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  • Community Rewards
    • Allocation & Schedule
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    • Distribution Formula
    • Conditional Liquid Staking Tokens: a Participation-based Vesting primitive
    • Game Theory of Reputation Mining
  • Reputation Finance
    • What is RepFi (Reputation Finance)
    • Social Prediction Market Making: Peer Staking
      • Parameters & Calculations
    • Unrealized Rep as a Collateral (URRC)
  • Conclusions
    • Conclusions
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  • Core Parameters
  • Gains —>
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  1. Reputation Finance
  2. Social Prediction Market Making: Peer Staking

Parameters & Calculations

Core Parameters

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

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

  • AjA_{j}Aj​: The "age" of the ĀutID of the stakee (j), represented by the sum of all periods in their Peer Value (υ\upsilonυ) history ( ∑TGj\sum T_{G_{j}}∑TGj​​).

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

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

  • fD‾Gjf\overline{D}{G_{j}}fDGj​: the amount of continuous segments of periods T, of the same length of D.

    • Calculated as: fD‾Gj=AjD‾Gjf\overline{D}{G_{j}} = \frac {A_{j}}{\overline{D}{G_{j}}}fDGj​=DGj​Aj​​, where:

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

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

    • GLi=1∑(D‾Gj≥EGj)fD‾Gj→GLi=fD‾Gj∑(D‾Gj≥EGj)\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})}GLi​=fDGj∑(DGj≥EGj​)​1​→GLi​=∑(DGj≥EGj​)fDGj​​​

    • or again, in prettier form:

    • GLi=fD‾Gj×(∑D‾Gj≥EGjEG)−1\displaystyle GL_{i} = f\overline D_{G_{j}} \times (\sum_{\tiny \overline{D} G_{j} \ge EG_{j}} EG)^{-1}GLi​=fDGj​​×(DGj​≥EGj​∑​EG)−1

Gains —> $Aˉ⊕\$Ā_{\tiny \oplus}$Aˉ⊕​

$Aˉ⊕={$Aˉ(staked)×1.5if ∑(D‾Gj≥EGj)=0$Aˉ(staked)×(1+GLi+DA)in all other cases \$Ā_{\oplus} = \begin{cases} \$Ā_{(staked)} \times 1.5 &\text{if } \sum{(\overline{D}}{G{j}}\ge EG_{j}) = 0 \\ \$Ā_{(staked)} \times (1 + GL_{i} + \frac {D}{A}) &\text{in all other cases } \end{cases}$Aˉ⊕​={$Aˉ(staked)​×1.5$Aˉ(staked)​×(1+GLi​+AD​)​if ∑(DGj≥EGj​)=0in all other cases ​

where:

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

Losses —> $Aˉ⊖\$Ā_{\tiny \ominus}$Aˉ⊖​

$Aˉ⊖={$Aˉ(staked)×0.75if ∑(D‾Gj≥EGj)=0$Aˉ(staked)×[1−(GLi+DA)]in all other cases \$Ā_{\ominus} = \begin{cases} \$Ā_{(staked)} \times 0.75 &\text{if } \sum{(\overline{D}}{G{j}}\ge EG_{j}) = 0 \\ \$Ā_{(staked)} \times [1 - (GL_{i} + \frac {D}{A})] &\text{in all other cases } \end{cases}$Aˉ⊖​={$Aˉ(staked)​×0.75$Aˉ(staked)​×[1−(GLi​+AD​)]​if ∑(DGj≥EGj​)=0in all other cases ​

where:

  • $Aˉ⊖\$Ā_{\ominus}$Aˉ⊖​ = $AUT losses

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Last updated 4 months ago