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documentation/specs/src/economics/inflation-system.md

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@@ -21,10 +21,10 @@ Inflation is calculated and paid per-epoch as follows.
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First, we start with the following fixed (governance-alterable) parameters:
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- $Cap_{PoS}$ is the cap of proof-of-stake reward rate, in units of percent per annum (genesis default: 10%)
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- $Cap_{SP-A}$ is the cap of shielded pool reward rate for each asset $A$, in units of percent per annum
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- $R_{PoS-Target}$ is the target staking ratio (genesis default: 2/3)
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- $R_{SP-A-Target}$ is the target amount of asset $A$ locked in the shielded pool (separate value for each asset $A$)
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- $Cap_{SP_A}$ is the cap of shielded pool reward rate for each asset $A$, in units of percent per annum
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- $\lambda_{PGF}$ is the public goods funding reward rate, in units of percent per annum
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- $R_{PoS-target}$ is the target staking ratio (genesis default: 2/3)
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- $R_{SP_A-target}$ is the target amount of asset $A$ locked in the shielded pool (separate value for each asset $A$)
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- $EpochsPerYear$ is the number of epochs per year (genesis default: 365)
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- ${KP}_{PoS-nom}$ is the nominal proportional gain of the proof-of-stake PD controller, as a fraction of the total input range
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- ${KD}_{PoS-nom}$ is the nominal derivative gain of the proof-of-stake PD controller, as a fraction of the total input range
@@ -49,10 +49,10 @@ These tokens are distributed to the public goods funding validity predicate.
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To run the PD-controllers for proof-of-stake and shielded pool rewards, we first calculate some intermediate values:
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- $Cap_{PoS-Epoch} := S_{NAM} * Cap_{PoS} / EpochsPerYear$
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- $Cap_{SP_A-Epoch} := S_{NAM} * Cap_{SP_A} / EpochsPerYear$ (separate value for each $A$)
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- Calculate the latest staking ratio $R_{PoS}$ as $L_{PoS} / S_{NAM}$
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- Calculate the per-epoch cap on the proof-of-stake and shielded pool token inflation
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- $Cap_{PoS-Epoch} = S_{NAM} * Cap_{PoS} / EpochsPerYear$
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- $Cap_{SP_A-Epoch} = S_{NAM} * Cap_{SP_A} / EpochsPerYear$ (separate value for each $A$)
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- Calculate PD-controller constants to be used for this epoch
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- ${KP}_{PoS} = {KP}_{PoS-nom} * Cap_{PoS-Epoch}$
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- ${KD}_{PoS} = {KD}_{PoS-nom} * Cap_{PoS-Epoch}$
@@ -61,7 +61,7 @@ To run the PD-controllers for proof-of-stake and shielded pool rewards, we first
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Then, for proof-of-stake first, run the PD-controller:
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- Calculate the error $E_{PoS} = R_{PoS-Target} - R_{PoS}$
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- Calculate the error $E_{PoS} = R_{PoS-target} - R_{PoS}$
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- Calculate the error derivative $E'_{PoS} = E_{PoS} - E_{PoS-last} = R_{PoS-last} - R_{PoS}$
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- Calculate the control value $C_{PoS} = (KP_{PoS} * E_{PoS}) - (KD_{PoS} * E'_{PoS})$
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- Calculate the new $I'_{PoS} = max(0, min(I_{PoS} + C_{PoS}, Cap_{PoS-Epoch}))$
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Similarly, for each asset $A$ for which shielded pool rewards are being paid:
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- Calculate the error $E_{SP_A} = R_{SP_A-Target} - R_{SP_A}$
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- Calculate the error $E_{SP_A} = R_{SP_A-target} - R_{SP_A}$
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- Calculate the error derivative $E'_{SP_A} = E_{SP_A} - E_{SP_A-last} = R_{SP_A-last} - R_{SP_A}$
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- Calculate the control value $C_{SP_A} = (KP_{SP_A} * E_{SP_A}) - (KD_{SP_A} * E'_{SP_A})$
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- Calculate the new $I'_{SP_A} = max(0, min(I_{SP_A} + C_{SP_A}, Cap_{SP_A-Epoch}))$
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These tokens are distributed to the shielded pool reward distribution validity predicate.
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Finally, we store the current inflation and error values for the next controller round.
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Finally, we store the latest inflation and locked token ratio values for the next epoch's controller round.

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