Added another economic sim

beacon_chain_impl/test_full_pos.py

@@ -6,7 +6,7 @@ import bls
 from simpleserialize import serialize, deserialize, eq, deepcopy
 import time
 
-privkeys = [int.from_bytes(blake(str(i).encode('utf-8'))[:4], 'big') for i in range(1000)]
+privkeys = [int.from_bytes(blake(str(i).encode('utf-8'))[:4], 'big') for i in range(100000)]
 print('Generated privkeys')
 keymap = {}
 for i,k in enumerate(privkeys):

economic_analysis/censorship_sim.py

@@ -0,0 +1,68 @@
+# 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])