augmented bonding curve version

bonding_curve_eq.py

@@ -0,0 +1,58 @@
+
+
+default_kappa= 2
+default_exit_tax = .02
+
+#value function for a given state (R,S)
+def invariant(R,S,kappa=default_kappa):
+    
+    return (S**kappa)/R
+
+#given a value function (parameterized by kappa)
+#and an invariant coeficient V0
+#return Supply S as a function of reserve R
+def reserve(S, V0, kappa=default_kappa):
+
+    return (S**kappa)/V0
+
+#given a value function (parameterized by kappa)
+#and an invariant coeficient V0
+#return Supply S as a function of reserve R
+def supply(R, V0, kappa=default_kappa):
+    return (V0*R)**(1/kappa)
+
+#given a value function (parameterized by kappa)
+#and an invariant coeficient V0
+#return a spot price P as a function of reserve R
+def spot_price(R, V0, kappa=default_kappa):
+    return kappa*R**((kappa-1)/kappa)/V0**(1/kappa)
+
+#for a given state (R,S)
+#given a value function (parameterized by kappa)
+#and an invariant coeficient V0
+#deposit deltaR to Mint deltaS
+#with realized price deltaR/deltaS
+def mint(deltaR, R,S, V0, kappa=default_kappa):
+    deltaS = (V0*(R+deltaR))**(1/kappa)-S
+    realized_price = deltaR/deltaS
+    return deltaS, realized_price
+
+#for a given state (R,S)
+#given a value function (parameterized by kappa)
+#and an invariant coeficient V0
+#burn deltaS to Withdraw deltaR
+#with realized price deltaR/deltaS
+def withdraw(deltaS, R,S, V0, kappa=default_kappa):
+    deltaR = R-((S-deltaS)**kappa)/V0
+    realized_price = deltaR/deltaS
+    return deltaR, realized_price
+
+def withdraw_with_tax(deltaS, R,S, V0, exit_tax = default_exit_tax, kappa=default_kappa):
+    deltaR = R-((S-deltaS)**kappa)/V0
+    
+    quantity_taxed = exit_tax*deltaR
+    quantity_recieved = (1-exit_tax)*deltaR
+    
+    realized_price = quantity_recieved/deltaS
+    
+    return quantity_recieved, quantity_taxed, realized_price

conviction_helpers.py

@@ -1,6 +1,7 @@
 import networkx as nx
 from scipy.stats import expon, gamma
 import numpy as np
+from bonding_curve_eq import reserve, invariant,spot_price
 import matplotlib.pyplot as plt
 import matplotlib.colors as colors
 import matplotlib.cm as cmx
@@ -12,13 +13,30 @@ def get_nodes_by_type(g, node_type_selection):
 def get_edges_by_type(g, edge_type_selection):
     return [edge for edge in g.edges if g.edges[edge]['type']== edge_type_selection ]
 
-def total_funds_given_total_supply(total_supply):
+default_theta = .25
+default_initial_price = .1
+default_kappa = 2
 
-    #can put any bonding curve invariant here for initializatio!
+def total_funds_given_total_supply(total_supply, theta = default_theta, initial_price = default_initial_price):
-    total_funds = total_supply**2/1000
+    
+    S = total_supply
+    total_funds = theta*reserve(S, S*initial_price)
     
     return total_funds
 
+def initialize_bonding_curve(initial_supply, initial_price = default_initial_price, kappa =default_kappa, theta = default_theta):
+    
+    S = initial_supply
+    R =  reserve(S, S*initial_price)*(1-theta)
+    
+    V0 = invariant(R,S,kappa)
+    
+    initial_reserve = R
+    
+    hatch_price = spot_price(R, V0, kappa)
+    
+    return initial_reserve, V0, hatch_price
+
 #maximum share of funds a proposal can take
 default_beta = .2 #later we should set this to be param so we can sweep it
 # tuning param for the trigger function

conviction_system_logic3.py

@@ -0,0 +1,554 @@
+import numpy as np
+from conviction_helpers import get_nodes_by_type, get_edges_by_type, social_affinity_booster
+from bonding_curve_eq import reserve, spot_price, withdraw_with_tax
+#import networkx as nx
+from scipy.stats import expon, gamma
+
+
+#functions for partial state update block 1
+
+#Driving processes: arrival of participants, proposals and funds
+##-----------------------------------------
+def gen_new_participant(network, new_participant_holdings):
+    
+    i = len([node for node in network.nodes])
+    
+    network.add_node(i)
+    network.nodes[i]['type']="participant"
+    
+    s_rv = np.random.rand() 
+    network.nodes[i]['sentiment'] = s_rv
+    network.nodes[i]['holdings']=new_participant_holdings
+    
+    for j in get_nodes_by_type(network, 'proposal'):
+        network.add_edge(i, j)
+        
+        rv = np.random.rand()
+        a_rv = 1-4*(1-rv)*rv #polarized distribution
+        network.edges[(i, j)]['affinity'] = a_rv
+        network.edges[(i,j)]['tokens'] = a_rv*network.nodes[i]['holdings']
+        network.edges[(i, j)]['conviction'] = 0
+        network.edges[(i,j)]['type'] = 'support'
+    
+    return network
+    
+
+
+
+def gen_new_proposal(network, funds, supply, trigger_func, scale_factor = 1.0/100):
+    
+    
+    
+    j = len([node for node in network.nodes])
+    network.add_node(j)
+    network.nodes[j]['type']="proposal"
+    
+    network.nodes[j]['conviction']=0
+    network.nodes[j]['status']='candidate'
+    network.nodes[j]['age']=0
+    
+    rescale = funds*scale_factor
+    r_rv = gamma.rvs(3,loc=0.001, scale=rescale)
+    network.node[j]['funds_requested'] = r_rv
+    
+    network.nodes[j]['trigger']= trigger_func(r_rv, funds, supply)
+    
+    participants = get_nodes_by_type(network, 'participant')
+    proposing_participant = np.random.choice(participants)
+    
+    for i in participants:
+        network.add_edge(i, j)
+        if i==proposing_participant:
+            network.edges[(i, j)]['affinity']=1
+        else:
+            rv = np.random.rand()
+            a_rv = 1-4*(1-rv)*rv #polarized distribution
+            network.edges[(i, j)]['affinity'] = a_rv
+            
+        network.edges[(i, j)]['conviction'] = 0
+        network.edges[(i,j)]['tokens'] = 0
+        network.edges[(i,j)]['type'] = 'support'
+        
+    return network
+        
+        
+
+def driving_process(params, step, sL, s):
+    
+    #placeholder plumbing for random processes
+    arrival_rate = 10/s['sentiment']
+    rv1 = np.random.rand()
+    new_participant = bool(rv1<1/arrival_rate)
+    supporters = get_edges_by_type(s['network'], 'support')
+    if new_participant:
+        h_rv = expon.rvs(loc=0.0, scale=1000)
+        new_participant_holdings = h_rv
+    else:
+        new_participant_holdings = 0
+    
+    network = s['network']
+    affinities = [network.edges[e]['affinity'] for e in supporters ]
+    median_affinity = np.median(affinities)
+    
+    proposals = get_nodes_by_type(network, 'proposal')
+    fund_requests = [network.nodes[j]['funds_requested'] for j in proposals if network.nodes[j]['status']=='candidate' ]
+    
+    funds = s['funds']
+    total_funds_requested = np.sum(fund_requests)
+    
+    proposal_rate = 10/median_affinity * total_funds_requested/funds
+    rv2 = np.random.rand()
+    new_proposal = bool(rv2<1/proposal_rate)
+    
+    sentiment = s['sentiment']
+    funds = s['funds']
+    scale_factor = funds*sentiment**2/10000
+    
+    #this shouldn't happen but expon is throwing domain errors
+    if sentiment>.4: 
+        funds_arrival = expon.rvs(loc = 0, scale = scale_factor )
+    else:
+        funds_arrival = 0
+    
+    return({'new_participant':new_participant,
+            'new_participant_holdings':new_participant_holdings,
+            'new_proposal':new_proposal, 
+            'funds_arrival':funds_arrival})
+
+    
+#Mechanisms for updating the state based on driving processes
+##---
+def update_network(params, step, sL, s, _input):
+
+    network = s['network']
+    funds = s['funds']
+    supply = s['supply']
+    trigger_func = params['trigger_func']
+    #print(trigger_func)
+
+    new_participant = _input['new_participant'] #T/F
+    new_proposal = _input['new_proposal'] #T/F
+
+    if new_participant:
+        new_participant_holdings = _input['new_participant_holdings']
+        network = gen_new_participant(network, new_participant_holdings)
+    
+    if new_proposal:
+        network= gen_new_proposal(network,funds,supply,trigger_func )
+    
+    #update age of the existing proposals
+    proposals = get_nodes_by_type(network, 'proposal')
+    
+    for j in proposals:
+        network.nodes[j]['age'] =  network.nodes[j]['age']+1
+        if network.nodes[j]['status'] == 'candidate':
+            requested = network.nodes[j]['funds_requested']
+            network.nodes[j]['trigger'] = trigger_func(requested, funds, supply)
+        else:
+            network.nodes[j]['trigger'] = np.nan
+            
+    key = 'network'
+    value = network
+    
+    return (key, value)
+
+def increment_funds(params, step, sL, s, _input):
+    
+    funds = s['funds']
+    funds_arrival = _input['funds_arrival']
+
+    #increment funds
+    funds = funds + funds_arrival
+    
+    key = 'funds'
+    value = funds
+    
+    return (key, value)
+
+def increment_supply(params, step, sL, s, _input):
+    
+    supply = s['supply']
+    supply_arrival = _input['new_participant_holdings']
+
+    #increment funds
+    supply = supply + supply_arrival
+    
+    key = 'supply'
+    value = supply
+    
+    return (key, value)
+
+#functions for partial state update block 2
+
+#Driving processes: completion of previously funded proposals
+##-----------------------------------------
+
+def check_progress(params, step, sL, s):
+    
+    network = s['network']
+    proposals = get_nodes_by_type(network, 'proposal')
+    
+    completed = []
+    failed = []
+    for j in proposals:
+        if network.nodes[j]['status'] == 'active':
+            grant_size = network.nodes[j]['funds_requested']
+            base_completion_rate=params['base_completion_rate']
+            likelihood = 1.0/(base_completion_rate+np.log(grant_size))
+            
+            base_failure_rate = params['base_failure_rate']
+            failure_rate = 1.0/(base_failure_rate+np.log(grant_size))
+            if np.random.rand() < likelihood:
+                completed.append(j)
+            elif np.random.rand() < failure_rate:
+                failed.append(j)
+    
+    return({'completed':completed, 'failed':failed})
+
+
+#Mechanisms for updating the state based on check progress
+##---
+def complete_proposal(params, step, sL, s, _input):
+    
+    network = s['network']
+    participants = get_nodes_by_type(network, 'participant')
+    proposals = get_nodes_by_type(network, 'proposal')
+    competitors = get_edges_by_type(network, 'conflict')
+    
+    completed = _input['completed']
+    for j in completed:
+        network.nodes[j]['status']='completed'
+
+        for c in proposals:
+             if (j,c) in competitors:
+                 conflict = network.edges[(j,c)]['conflict']
+                 for i in participants:
+                     network.edges[(i,c)]['affinity'] = network.edges[(i,c)]['affinity'] *(1-conflict)
+
+        for i in participants:
+            force = network.edges[(i,j)]['affinity']
+            sentiment = network.node[i]['sentiment']
+            network.node[i]['sentiment'] = get_sentimental(sentiment, force, decay=0)
+
+                
+    
+    failed = _input['failed']
+    for j in failed:
+        network.nodes[j]['status']='failed' 
+        for i in participants:
+            force = -network.edges[(i,j)]['affinity']
+            sentiment = network.node[i]['sentiment']
+            network.node[i]['sentiment'] = get_sentimental(sentiment, force, decay=0)
+    
+    key = 'network'
+    value = network
+    
+    return (key, value)
+
+def update_sentiment_on_completion(params, step, sL, s, _input):
+    
+    network = s['network']
+    proposals = get_nodes_by_type(network, 'proposal')
+    completed = _input['completed']
+    failed = _input['failed']
+    
+    grants_outstanding = np.sum([network.nodes[j]['funds_requested'] for j in proposals if network.nodes[j]['status']=='active'])
+    
+    grants_completed = np.sum([network.nodes[j]['funds_requested'] for j in completed])
+    grants_failed = np.sum([network.nodes[j]['funds_requested'] for j in failed])
+    
+    sentiment = s['sentiment']
+    
+    if grants_outstanding>0:
+        force = (grants_completed-grants_failed)/grants_outstanding
+    else:
+        force=1
+    mu = params['sentiment_decay']
+    if (force >=0) and (force <=1):
+        sentiment = get_sentimental(sentiment, force, mu)
+    else:
+        sentiment = get_sentimental(sentiment, 0, mu)
+    
+    
+    key = 'sentiment'
+    value = sentiment
+    
+    return (key, value)
+
+def get_sentimental(sentiment, force, decay=0):
+    mu = decay
+    sentiment = sentiment*(1-mu) + force
+    
+    if sentiment > 1:
+        sentiment = 1
+        
+    return sentiment
+
+#functions for partial state update block 3
+
+#Decision processes: trigger function policy
+##-----------------------------------------
+
+def trigger_function(params, step, sL, s):
+    
+    network = s['network']
+    funds = s['funds']
+    supply = s['supply']
+    proposals = get_nodes_by_type(network, 'proposal')
+    tmin = params['tmin']
+    trigger_func = params['trigger_func']
+    
+    accepted = []
+    triggers = {}
+    for j in proposals:
+        if network.nodes[j]['status'] == 'candidate':
+            requested = network.nodes[j]['funds_requested']
+            age = network.nodes[j]['age']
+            threshold = trigger_func(requested, funds, supply)
+            if age > tmin:
+                conviction = network.nodes[j]['conviction']
+                if conviction >threshold:
+                    accepted.append(j)
+        else:
+            threshold = np.nan
+            
+        triggers[j] = threshold
+                    
+    return({'accepted':accepted, 'triggers':triggers})
+    
+#functions for partial state update block 3
+
+#state updates
+##---
+
+def decrement_funds(params, step, sL, s, _input):
+    
+    funds = s['funds']
+    network = s['network']
+    accepted = _input['accepted']
+
+    #decrement funds
+    for j in accepted:
+        funds = funds - network.nodes[j]['funds_requested']
+    
+    key = 'funds'
+    value = funds
+    
+    return (key, value)
+
+def update_proposals(params, step, sL, s, _input):
+    
+    network = s['network']
+    accepted = _input['accepted']
+    triggers = _input['triggers']
+    participants = get_nodes_by_type(network, 'participant')
+    proposals = get_nodes_by_type(network, 'proposals')
+    sensitivity = params['sensitivity']
+    
+    for j in proposals:
+        network.nodes[j]['trigger'] = triggers[j]
+    
+    #bookkeeping conviction and participant sentiment
+    for j in accepted:
+        network.nodes[j]['status']='active'
+        network.nodes[j]['conviction']=np.nan
+        #change status to active
+        for i in participants:
+        
+            #operating on edge = (i,j)
+            #reset tokens assigned to other candidates
+            network.edges[(i,j)]['tokens']=0
+            network.edges[(i,j)]['conviction'] = np.nan
+            
+            #update participants sentiments (positive or negative) 
+            affinities = [network.edges[(i,p)]['affinity'] for p in proposals if not(p in accepted)]
+            if len(affinities)>1:
+                max_affinity = np.max(affinities)
+                force = network.edges[(i,j)]['affinity']-sensitivity*max_affinity
+            else:
+                force = 0
+            
+            #based on what their affinities to the accepted proposals
+            network.nodes[i]['sentiment'] = get_sentimental(network.nodes[i]['sentiment'], force, False)
+            
+    
+    key = 'network'
+    value = network
+    
+    return (key, value)
+
+def update_sentiment_on_release(params, step, sL, s, _input):
+    
+    network = s['network']
+    proposals = get_nodes_by_type(network, 'proposal')
+    accepted = _input['accepted']
+    
+    proposals_outstanding = np.sum([network.nodes[j]['funds_requested'] for j in proposals if network.nodes[j]['status']=='candidate'])
+    
+    proposals_accepted = np.sum([network.nodes[j]['funds_requested'] for j in accepted])
+    
+    sentiment = s['sentiment']
+    force = proposals_accepted/proposals_outstanding
+    if (force >=0) and (force <=1):
+        sentiment = get_sentimental(sentiment, force, False)
+    else:
+        sentiment = get_sentimental(sentiment, 0, False)
+    
+    key = 'sentiment'
+    value = sentiment
+    
+    return (key, value)
+
+
+#functions for partial state update block 4
+
+#Decision processes: trigger function policy
+##---
+def participants_decisions(params, step, sL, s):
+    
+    network = s['network']
+    participants = get_nodes_by_type(network, 'participant')
+    proposals = get_nodes_by_type(network, 'proposal')
+    candidates = [j for j in proposals if network.nodes[j]['status']=='candidate']
+    sensitivity = params['sensitivity']
+    
+    gain = .01
+    delta_holdings={}
+    proposals_supported ={}
+    for i in participants:
+        
+        engagement_rate = .3*network.nodes[i]['sentiment']
+        if np.random.rand()<engagement_rate:
+        
+            force = network.nodes[i]['sentiment']-sensitivity
+            delta_holdings[i] = network.nodes[i]['holdings']*gain*force
+            
+            support = []
+            for j in candidates:
+                affinity = network.edges[(i, j)]['affinity']*.5+.5*social_affinity_booster(network, j, i) 
+                cutoff = sensitivity*np.max([network.edges[(i,p)]['affinity'] for p in candidates])
+                if cutoff <.5:
+                    cutoff = .5
+                
+                if affinity > cutoff:
+                    support.append(j)
+            
+            proposals_supported[i] = support
+        else:
+            delta_holdings[i] = 0
+            proposals_supported[i] = [j for j in candidates if network.edges[(i,j)]['tokens']>0 ]
+    
+    return({'delta_holdings':delta_holdings, 'proposals_supported':proposals_supported})
+
+#functions for partial state update block 4
+
+#state updates
+##---
+
+def update_tokens(params, step, sL, s, _input):
+    
+    network = s['network']
+    delta_holdings = _input['delta_holdings']
+    proposals = get_nodes_by_type(network, 'proposal')
+    candidates = [j for j in proposals if network.nodes[j]['status']=='candidate']
+    proposals_supported = _input['proposals_supported']
+    participants = get_nodes_by_type(network, 'participant')
+    alpha = params['alpha']
+    min_support = params['min_supp']
+    
+    for i in participants:
+        network.nodes[i]['holdings'] = network.nodes[i]['holdings']+delta_holdings[i]
+        supported = proposals_supported[i]
+        total_affinity = np.sum([ network.edges[(i, j)]['affinity'] for j in supported])
+        for j in candidates:
+            if j in supported:
+                normalized_affinity = network.edges[(i, j)]['affinity']/total_affinity
+                network.edges[(i, j)]['tokens'] = normalized_affinity*network.nodes[i]['holdings']
+            else:
+                network.edges[(i, j)]['tokens'] = 0
+            
+            prior_conviction = network.edges[(i, j)]['conviction']
+            current_tokens = network.edges[(i, j)]['tokens']
+            network.edges[(i, j)]['conviction'] =current_tokens+alpha*prior_conviction
+    
+    for j in candidates:
+        network.nodes[j]['conviction'] = np.sum([ network.edges[(i, j)]['conviction'] for i in participants])
+        total_tokens = np.sum([network.edges[(i, j)]['tokens'] for i in participants ])
+        if total_tokens < min_support:
+            network.nodes[j]['status'] = 'killed'
+    
+    key = 'network'
+    value = network
+    
+    return (key, value)
+
+#organizing the bonding curve into a nested state would
+    #make this code more efficient, lots of duplicated logic here
+
+def update_supply(params, step, sL, s, _input):
+    
+    supply = s['supply']
+    delta_holdings = _input['delta_holdings']
+    delta_supply = np.sum([v for v in delta_holdings.values()])
+    
+    supply = supply + delta_supply
+    
+    key = 'supply'
+    value = supply
+    
+    return (key, value)
+
+def update_reserve(params, step, sL, s, _input):
+    
+    supply = s['supply']
+    delta_holdings = _input['delta_holdings']
+    delta_supply = np.sum([v for v in delta_holdings.values()])
+    supply = supply + delta_supply
+    
+    kappa = params['kappa']
+    V0 = params['invariant']
+    
+    R = reserve(supply, V0, kappa)
+    
+    key = 'reserve'
+    value = R
+    
+    return (key, value)
+
+def update_price(params, step, sL, s, _input):
+    
+    supply = s['supply']
+    delta_holdings = _input['delta_holdings']
+    delta_supply = np.sum([v for v in delta_holdings.values()])
+    supply = supply + delta_supply
+    
+    kappa = params['kappa']
+    V0 = params['invariant']
+    
+    R = reserve(supply, V0, kappa)
+    price = spot_price(R, V0, kappa)
+    
+    key = 'spot_price'
+    value = price
+    
+    return (key, value)
+
+def update_funds(params, step, sL, s, _input):
+    
+    delta_holdings = _input['delta_holdings']
+    S = s['supply']
+    R = s['reserve']
+    V0=params['invariant']
+    kappa = params['kappa']
+    exit_tax = params['tax_rate']
+    #to avoid overestimating taxes well treat all withdraw before mint
+    wDS = np.sum([v for v in delta_holdings.values() if v<0])
+              
+    _,tax, _ = withdraw_with_tax(wDS, R,S, V0, exit_tax, kappa)
+    
+    funds = s['funds']+ tax
+    
+    key = 'funds'
+    value = funds
+    
+    return (key, value)