Is there a penalty for having a ETH 2.0 Staking node go down?

Question

For some proof of stake blockchain systems, there is a penalty if the node goes down during staking. Will there be some sort of penalty if an ETH 2.0 staking node went down? And if there isn't how does it stop stakers from power up and down their node to mess with the network?

Answer 1

Yes there are penalties for being offline. In "normal" (non-activity leak) circumstances, a validator loses approximately 15.8% of their stake per year they are offline. That's ~1.4% for being offline for a month or ~0.3% for being offline for a week.

Specifically, validators that fail to create attestations will suffer penalties. When the network is failing to finalize (as mentioned by @lauri-peltonen) those penalties are much more severe. These severe penalties are also refered to as the "inactivity leak" which is intended to quickly eject (by means of reducing balance) offline validators so the online validators can form a majority and resume finalization.

The calculation of penalties in Eth2 is not straight-forward; along with the inactivity-leak, the penalties also take into account the balance of the validator and the total balance of all validators. To arrive at the 15.8% number I used the following script that I derived from v0.11.1 of the canonical Eth2 specification:

DEPOSIT_AMOUNT = 32 * 10**9
VALIDATOR_COUNT = 16384
BASE_REWARD_FACTOR = 64
BASE_REWARDS_PER_EPOCH = 4
SECONDS_PER_SLOT = 12
SLOTS_PER_EPOCH = 32
SECONDS_PER_YEAR = 31557600
EPOCHS_PER_YEAR =  SECONDS_PER_YEAR // (SECONDS_PER_SLOT * SLOTS_PER_EPOCH)

def integer_squareroot(n):
    """
    Return the largest integer ``x`` such that ``x**2 <= n``.
    """
    x = n
    y = (x + 1) // 2
    while y < x:
        x = y
        y = (x + n // x) // 2
    return x

def get_base_reward(total_balance, effective_balance):
    return effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance) // BASE_REWARDS_PER_EPOCH

total_balance = DEPOSIT_AMOUNT * VALIDATOR_COUNT
validator_balance = DEPOSIT_AMOUNT

for _ in range(EPOCHS_PER_YEAR):
    penalty = get_base_reward(total_balance, validator_balance) * 3
    validator_balance -= penalty
    total_balance -= penalty

total_penalty = DEPOSIT_AMOUNT - validator_balance

print("Final balance: {}".format(validator_balance))
print("Total penalty: {}".format(total_penalty))
print("Reduction %: {}".format(100 * total_penalty / DEPOSIT_AMOUNT))

The output of this script is:

Final balance: 26935963853
Total penalty: 5064036147
Reduction %: 15.825112959375

This is a very rough approximation (some factors like hysteresis are ignored) and the 15.8% number is very subjective. In the real-world it's likely that the total_balance will increase as existing validators earn rewards and new validators join. Conversely, it's possible that the total balance will decrease and penalties will increase due to an inactivity-leak.

Whilst you can't trust this 15.8% p/a penalty to be constant, you can hopefully get an idea about the magnitude of the offline penalty.

Note: these values were previously off by a factor of 3, they have been updated now. My apologies.

Answer 2

Yes there is a penalty for being offline. A quote from article at https://ethos.dev/beacon-chain/ :

Basically, if there have been more than four epochs since finality, all validators suffer an inactivity penalty that increases quadratically until a checkpoint is finalized

You can check earlier in the article what an "epoch" means.