[research/lotterysim] apy

script/research/lotterysim/constants.py

@@ -4,20 +4,18 @@ N_TERM = 2
 CONTROLLER_TYPE_ANALOGUE=-1
 CONTROLLER_TYPE_DISCRETE=0
 CONTROLLER_TYPE_TAKAHASHI=1
+ERC20DRK=2.1*10**9
 
 L = 28948022309329048855892746252171976963363056481941560715954676764349967630337.0
-N_TERM = 2
-REWARD = 1
-BASE_L = L*0.01
-F_MIN = 0.00001
-F_MAX = 0.99999
+REWARD = 33
+F_MIN = 0.0001
+F_MAX = 0.9999
 EPSILON = 1
 
-L_HP = Num(28948022309329048855892746252171976963363056481941560715954676764349967630337.0)
-REWARD_HP = Num(1)
-BASE_L_HP = L_HP*Num(0.01)
-F_MIN_HP = Num(0.00001)
-F_MAX_HP = Num(0.99999)
-EPSILON_HP = Num(1)
-
-ERC20DRK=2.1*10**9
+L_HP = Num(L)
+REWARD_HP = Num(REWARD)
+F_MIN_HP = Num(F_MIN)
+F_MAX_HP = Num(F_MAX)
+EPSILON_HP = Num(EPSILON)
+SLOT = 90
+ONE_YEAR = 365.25*24*60*60/SLOT

script/research/lotterysim/darkie.py

@@ -2,12 +2,12 @@ from utils import *
 from threading import Thread
 
 class Darkie(Thread):
-    def __init__(self, airdrop, vesting=[], hp=False, commit=True, epoch_len=100):
+    def __init__(self, airdrop, initial_stake=None, vesting=[], hp=False, commit=True, epoch_len=100):
         Thread.__init__(self)
         self.vesting = [0] + vesting
         self.stake = (Num(airdrop) if hp else airdrop)
         self.initial_stake = self.stake # for debugging purpose
-        self.finalized_stake = (Num(airdrop) if hp else airdrop) # after fork finalization
+        self.finalized_stake = (Num(airdrop) if hp else airdrop) if initial_stake==None else (Num(initial_stake) if hp else initial_stake) # after fork finalization
         self.Sigma = None
         self.feedback = None
         self.f = None
@@ -16,9 +16,18 @@ class Darkie(Thread):
         self.epoch_len=epoch_len # epoch length during which the stake is static
         self.staked_tokens_ratio = 1 # ratio of staked tokens, if commit is true then it's 100%
         self.slot = 0
+
     def clone(self):
         return Darkie(self.finalized_stake)
 
+    def apy(self):
+        # approximation to APY assuming linear relation
+        # note! relation is logarithmic depending on PID output.
+        return Num(self.stake - self.initial_stake) / Num(self.initial_stake)
+
+    def apy_percentage(self):
+        return self.apy()*100
+
     def set_sigma_feedback(self, sigma, feedback, f, count, hp=True):
         self.Sigma = (Num(sigma) if hp else sigma)
         self.feedback = (Num(feedback) if hp else feedback)

script/research/lotterysim/f.hist

@@ -1 +0,0 @@
-0,0.7290000000000001,0.6561,0.6841000000000664,0.654299999646183,0.7121000000001328,0.6073000000000567,0.654299999646183,0.7206999996462543,0.673700000000128,0.5987000003539352,0.5792999999999903,0.6669000007078235,0.48710000106155465,0.4975000010614932,0.5445000007076195,0.6109000007076908,0.5639000010615645,0.49750000106149317,0.5445000007076195,0.6023000010615693,0.4975000010614931,0.5445000007076194,0.6023000010615692,0.48890000141537154,0.46090000141530524,0.49930000141531017,0.5079000010614316,0.5829000007076244,0.6195000003538123,0.6561000000000001,0.6755000003539451,0.5621000007077475,0.534100000707681,0.5811000003538074,0.6303000010616358,0.4591000010614883,0.5445000007076196,0.6023000010615694,0.47170000212312885,0.3195000017690414,0.5097000014152488,0.5377000014153153,0.49930000141531033,0.49930000141531033,0.5079000010614317,0.5657000014153816,0.46090000141530535,0.5079000010614317,0.5829000007076245,0.6109000007076909,0.5811000003538075,0.6475000003538788,0.6176999999999954,0.6755000003539452,0.5792999999999905,0.6926999996461881,0.729299999292376,0.7658999989385639,0.7938999989386303,0.7554999989386254,0.7554999989386254,0.7554999989386254,0.746899999292504,0.6890999989385541,0.7938999989386303,0.7554999989386254,0.7640999985847469,0.8218999989386967,0.7084999992924991,0.6633000000001897,0.5774999996461736,0.7206999996462548,0.6908999992923713,0.7572999992924426,0.7188999992924378,0.7188999992924378,0.7274999989385592,0.802499998584752,0.8218999989386969,0.7170999989386208,0.7554999989386256,0.7468999992925042,0.6804999992924329,0.7188999992924378,0.7274999989385592,0.785299999292509,0.6718999996463114,0.6353000000001235,0.6073000000000571,0.6371000003539405,0.5707000003538693,0.6091000003538741,0.6091000003538741,0.6091000003538741,0.6176999999999956,0.6926999996461883,0.7206999996462548,0.6908999992923713,0.7486999996463212,0.6524999992923665,

script/research/lotterysim/instance.py

@@ -4,16 +4,24 @@ import numpy
 os.system("rm f.hist; rm leads.hist")
 
 RUNNING_TIME = int(input("running time:"))
+
 NODES=1000
-ERC20DRK = 2.1*10**9
 
 if __name__ == "__main__":
-    darkies = [ Darkie(random.gauss(ERC20DRK/NODES, ERC20DRK/NODES*0.1)) for id in range(NODES) ]
+    darkies = []
+    egalitarian = ERC20DRK/NODES
+    darkies += [ Darkie(random.gauss(egalitarian, egalitarian*0.1)) for id in range(int(NODES)) ]
+    darkies += [Darkie(0) for _ in range(NODES)]
     airdrop = ERC20DRK
-    print("network airdrop: {} on {} nodes".format(airdrop, len(darkies)))
+    effective_airdrop  = 0
+    for darkie in darkies:
+        effective_airdrop+=darkie.stake
+    print("network airdrop: {}, staked token: {}/{}% on {} nodes".format(airdrop, effective_airdrop, effective_airdrop/airdrop*100, len(darkies)))
     dt = DarkfiTable(airdrop, RUNNING_TIME, CONTROLLER_TYPE_DISCRETE, kp=-0.010399999999938556, ki=-0.0365999996461878, kd=0.03840000000000491)
     for darkie in darkies:
         dt.add_darkie(darkie)
     acc = dt.background(rand_running_time=False)
+    sum_zero_stake = sum([darkie.stake for darkie in darkies[NODES:]])
     print('acc: {}'.format(acc))
+    print('total stake of 0mint: {}, ration: {}'.format(sum_zero_stake, sum_zero_stake/ERC20DRK))
     dt.write()

script/research/lotterysim/leads.hist

@@ -1 +0,0 @@
-0,0,0,0,1,0,2,1,0,1,2,2,0,3,2,1,0,1,2,1,0,2,1,0,2,2,1,1,0,0,0,0,2,2,1,0,3,1,0,2,4,0,0,1,1,1,0,2,1,0,0,1,0,1,0,2,0,0,0,0,1,1,1,1,2,0,1,1,0,2,2,3,0,1,0,1,1,1,0,0,2,1,1,2,1,1,0,2,2,2,1,2,1,1,1,1,0,0,1,0,2,0,

script/research/lotterysim/one_year_reward.py

@@ -0,0 +1,37 @@
+from lottery import *
+import os
+import numpy
+from matplotlib import pyplot as plt
+
+os.system("rm f.hist; rm leads.hist")
+
+RUNNING_TIME = 100000
+NODES=1000
+NORM_NODES = NODES/10
+
+stakes =  [100, 1000, 10000, 100000]
+rewards = []
+airdrop = ERC20DRK
+
+for stake in stakes:
+    effective_airdrop  = 0
+    darkies = []
+    norm_staker_sum = stake*NORM_NODES
+    egalitarian = (ERC20DRK-norm_staker_sum)/NODES
+    darkies += [ Darkie(random.gauss(egalitarian, egalitarian*0.1)) for id in range(int(NODES)) ]
+    darkies += [Darkie(stake) for _ in range(int(NORM_NODES))]
+    for darkie in darkies:
+        effective_airdrop+=darkie.stake
+    dt = DarkfiTable(effective_airdrop, RUNNING_TIME, CONTROLLER_TYPE_DISCRETE, kp=-0.010399999999938556, ki=-0.0365999996461878, kd=0.03840000000000491)
+    for darkie in darkies:
+        dt.add_darkie(darkie)
+    acc = dt.background(rand_running_time=False)
+    sum_zero_stake = sum([darkie.stake for darkie in darkies[NODES:]])
+    avg_zero_stake = sum_zero_stake/NORM_NODES
+    reward = ((avg_zero_stake/stake)-1)
+    print("stake: {}, acc: {}, reward: {}%".format(stake, acc*100, reward*100))
+    rewards += [(stake, reward)]
+print('avg rwards: {}%'. format(sum([r[1] for r in rewards])/len(stakes)))
+
+plt.plot([r[0] for r in rewards], [r[1] for r in rewards])
+plt.show()

script/research/lotterysim/stake_reward.py

@@ -0,0 +1,30 @@
+# running time ONE_YEAR
+#network airdrop: 2100000000.0, staked token: 2099223067.1631408/99.9630031982448% on 1000 nodes
+#acc: 37.5249500998004, reward: 0.0005964171059733166794378382704% with instant finality: 0.001589388138790594006649208260%
+
+from lottery import *
+import os
+import numpy
+
+os.system("rm f.hist; rm leads.hist")
+
+RUNNING_TIME = ONE_YEAR
+NODES=1000
+
+rewards = []
+airdrop = ERC20DRK
+darkies = []
+
+
+effective_airdrop  = 0
+egalitarian = ERC20DRK/NODES
+darkies = [ Darkie(random.gauss(egalitarian, egalitarian*0.01)) for id in range(int(NODES)) ]
+for darkie in darkies:
+    effective_airdrop+=darkie.stake
+print("network airdrop: {}, staked token: {}/{}% on {} nodes".format(airdrop, effective_airdrop, effective_airdrop/airdrop*100, len(darkies)))
+dt = DarkfiTable(effective_airdrop, RUNNING_TIME, CONTROLLER_TYPE_DISCRETE, kp=-0.010399999999938556, ki=-0.0365999996461878, kd=0.03840000000000491)
+for darkie in darkies:
+    dt.add_darkie(darkie)
+acc = dt.background(rand_running_time=False)
+apy_per = sum([darkie.apy_percentage() for darkie in darkies])/NODES
+print("acc: {}, reward: {}% with instant finality: {}%".format(acc*100, apy_per, apy_per/Num(acc)))

script/research/lotterysim/stake_rewards.txt

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script/research/lotterysim/utils.py

@@ -14,7 +14,6 @@ def fact(n, hp=False):
     else:
         return (Num(n) if hp else n)* fact(n-1, hp)
 
-
 # all inputs to this function are integers
 # sigmas are public
 # stake is private
@@ -25,7 +24,7 @@ def approx_target_in_zk(sigmas, stake):
     # secondly the reward, or at least the total stake in the network,
     # can't be anonymous, should be public.
     T = [sigma*(stake)**(i+1) for i, sigma in enumerate(sigmas)]
-    return -1*sum(T)
+    return -1*sum(T) #+ F_MIN_HP*L_HP
 
 def rnd(hp=False):
     return Num(random.random()) if hp else random.random()