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