69 lines
2.5 KiB
Python
69 lines
2.5 KiB
Python
# Total ETH supply
|
|
total_supply = 10**8
|
|
|
|
# Returns to online validators, based on perceived fraction online
|
|
def R(p):
|
|
return p**1.53
|
|
|
|
# Returns to offline validators, based on perceived fraction online
|
|
def P(p):
|
|
return 0
|
|
|
|
# What interest rate are `deposits` ETH worth of validators willing to accept?
|
|
def demand_curve(deposits):
|
|
return deposits / total_supply / 10
|
|
|
|
# Given a total deposit size, and a fraction online, compute the interest
|
|
# paid to each online and offline validator
|
|
def get_rewards(deposits, p_online):
|
|
# Total txfees
|
|
fees = 50000
|
|
# Portion of fees that get "reclaimed" by the protocol
|
|
reclaimed = 0.5
|
|
# The un-reclaimed fees, which are necessarily distributed among
|
|
# the online validators
|
|
uncontrolled_reward = fees * (1 - reclaimed) / deposits / p_online
|
|
# The reclaimed fees, minus a portion that gets held back based on
|
|
# the portion of ETH holders staking
|
|
max_controlled_rewards = fees * reclaimed * \
|
|
(deposits / total_supply) ** 0.8
|
|
# In the best possible case (100% online), everyone gets R(1) interest.
|
|
# Rescale interest based on this.
|
|
controlled_rewards_multiplier = max_controlled_rewards / deposits / R(1)
|
|
# Return computed interest
|
|
return uncontrolled_reward + controlled_rewards_multiplier * R(p_online), \
|
|
controlled_rewards_multiplier * P(p_online)
|
|
|
|
# Total deposits in the validator set
|
|
deposits = 1000000
|
|
|
|
# Find the pre-attack equilibrium
|
|
for i in range(100):
|
|
interest, _ = get_rewards(deposits, 1)
|
|
if interest < demand_curve(deposits):
|
|
deposits -= 10000
|
|
else:
|
|
deposits += 10000
|
|
|
|
attacker = deposits * 0.501
|
|
print('Baseline total deposits:', deposits)
|
|
print('Baseline interest:', get_rewards(deposits, 1)[0])
|
|
print('Baseline attacker revenue:', get_rewards(deposits, 1)[0] * attacker)
|
|
print('Baseline victim revenue:', get_rewards(deposits, 1)[0] * (deposits - attacker))
|
|
|
|
# Start the attack. Find the post-attack equilibrium.
|
|
for i in range(1000):
|
|
attacker_share = attacker / deposits
|
|
atk_interest, vic_interest = get_rewards(deposits, attacker_share)
|
|
if vic_interest < demand_curve(deposits):
|
|
deposits -= min(10000, deposits - attacker)
|
|
else:
|
|
deposits += 10000
|
|
|
|
print('New total deposits:', deposits)
|
|
print('Attacker share:', attacker_share)
|
|
print('Victim interest:', vic_interest)
|
|
print('Attacker interest:', atk_interest)
|
|
print('Attacker revenue:', atk_interest * attacker)
|
|
print('Possible non-attacking revenue:', get_rewards(deposits, 1)[0])
|