Example Staking Dynamics
To illustrate the dynamics of this system, consider a toy scenario with three delegators, Alice, Bob, and Charlie, and two validators, Victoria and William. Tendermint consensus requires at least four validators and no one party controlling more than of the stake, but this example uses only a few parties just to illustrate the dynamics.
For simplicity, the base reward rates and commission rates
are fixed over all epochs at and , .
The PEN
and dPEN
holdings of participant are
denoted by , , etc., respectively.
Alice starts with dPEN
of Victoria’s delegation pool, Bob starts
with dPEN
of William’s delegation pool, and Charlie starts with
unbonded PEN
.
-
At genesis, Alice, Bob, and Charlie respectively have fractions , , and of the total stake, and fractions , , of the total voting power.
-
At epoch , Alice, Bob, and Charlie’s holdings remain unchanged, but their unrealized notional values have changed.
- Victoria charges zero commission, so . Alice’s
dPEN(v)
is now worthPEN
. - William charges commission, so . Bob’s
dPEN(w)
is now worth , and William receivesPEN
. - William can use the commission to cover expenses, or self-delegate. In this example, we assume that validators self-delegate their entire commission, to illustrate the staking dynamics.
- William self-delegates
PEN
, to getdPEN
in the next epoch, epoch .
- Victoria charges zero commission, so . Alice’s
-
At epoch :
- Alice’s
dPEN(v)
is now worthPEN
. - Bob’s
dPEN(w)
is now worthPEN
. - William’s self-delegation of accumulated commission has resulted in
dPEN(w)
. - Victoria’s delegation pool remains at size
dPEN(v)
. William’s delegation pool has increased todPEN(w)
. However, their respective adjustment factors are now and , so the voting powers of their delegation pools are respectively and .- The slight loss of voting power for William’s delegation pool occurs because William self-delegates rewards with a one epoch delay, thus missing one epoch of compounding.
- Charlie’s unbonded
PEN
remains unchanged, but its value relative to Alice and Bob’s bonded stake has declined. - William’s commission transfers stake from Bob, whose voting power has slightly declined relative to Alice’s.
- The distribution of stake between Alice, Bob, Charlie, and William is now , , , respectively. The distribution of voting power is , , , respectively.
- Charlie decides to bond his stake, split evenly between Victoria and William, to get
dPEN(v)
anddPEN(w)
.
- Alice’s
-
At epoch :
- Charlie now has
dPEN(v)
anddPEN(w)
, worthPEN
. - For the same amount of unbonded stake, Charlie gets more
dPEN(w)
thandPEN(v)
, because the exchange rate prices in the cumulative effect of commission since genesis, but Charlie isn’t charged for commission during the time he didn’t delegate to William. - William’s commission for this epoch is now
PEN
, up fromPEN
in the previous epoch. - The distribution of stake between Alice, Bob, Charlie, and William is now , , , respectively. Because all stake is now bonded, except William’s commission for this epoch, which is insignificant, the distribution of voting power is identical to the distribution of stake.
- Charlie now has
-
At epoch :
- Alice’s
dPEN(v)
is now worthPEN
. - Bob’s
dPEN(w)
is now worthPEN
. - Charlies’s
dPEN(v)
is now worthPEN
, and hisdPEN(w)
is now worthPEN
. - William’s self-delegation of accumulated commission has resulted in
dPEN(w)
, worthPEN
. - The distribution of stake and voting power between Alice, Bob, Charlie, and William is now , , , respectively.
- Alice’s
This scenario was generated with a model in this Google Sheet.