Validator Rewards and Fees

Validators declare a set of funding streams that comprise the destination of all of their staking rewards. Each funding stream contains a rate $r_i\in [0,1]$ and a destination address $a_i$. The validator’s total commission rate is defined as $c_{v,e}=\sum r_i$, the sum of the rate of each funding stream. $c_{v,e}$ cannot exceed 1.

The spread between the base reward rate $r_e$ and the reward rate for their delegators is determined by the validator’s total commission $r_{v,e}=(1-c_{v,e})r_e$, or equivalently $r_e=r_{v,e}+c_{v,e}{r}_e$.

Validator rewards are distributed in the first block of each epoch. In epoch $e$, a validator $v$ whose delegation pool has size $y_v$ dPEN receives a commission of size $$y_v{c}_{v,e}{r}_e\psi (e-1)$$ PEN, issued to the validator’s address.

To see why this is the reward amount, suppose validator $v$ has a delegation pool of size $y_v$ dPEN. In epoch $e-1$, the value of the pool is $y_v{\psi }_v(e-1)$ PEN. In epoch $e$, the base reward rate $r_e$ causes the value of the pool to increase to $$(1+r_e)y_v{\psi }_v(e-1).$$ Splitting $r_e$ as $r_e=r_{v,e}+c_{v,e}{r}_e$, this becomes $$y_v(1+r_{v,e}){\psi }_v(e-1)+c_{v,e}{r}_e{y}_v{\psi }_v(e-1).$$

The value in the first term, $y_v(1+r_{v,e}){\psi }_v(e-1)$, corresponds to the $r_{v,e}$ portion, and accrues to the delegators. Since $(1+r_{v,e}){\psi }_v(e-1)={\psi }_v(e)$, this is exactly $y_v{\psi }_v(e)$, the new PEN-denominated value of the delegation pool.

The value in the second term, $c_{v,e}{r}_e{y}_v{\psi }_v(e-1)$, corresponds to the $c_{v,e}{r}_e$ portion, and accrues to the validator as commission. Validators can self-delegate the resulting PEN or use it to fund their operating expenses.

Transaction fees are denominated in PEN and are burned, so that the value of the fees accrues equally to all stake holders.

TODO

• allow transaction fees in dPEN with appropriate price adjustment, but only in transactions (e.g., undelegations, voting) that otherwise reveal the flavor of dPEN, so that there is no additional distinguisher?