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@cello-kabob cello-kabob/PDsemi.py Secret

Created Jun 30, 2020
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Code used to generate and analyze the prisoner's dilemma as a transformation semigroup.

The .py file is used to generate semigroup mappings for each regime which can be used as input to GAP (https://www.gap-system.org/) The .g file can then be read into GAP for analysis and figure generation.

#this can be changed to include any of the constant mappings (d1-d6, c1-c6)
PD:=Semigroup(t);
#PDstates:=["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63"];
PDstates:=["000000", "000001", "000010", "000011", "000100", "000101", "000110", "000111", "001000", "001001", "001010", "001011", "001100", "001101", "001110", "001111", "010000", "010001", "010010", "010011", "010100", "010101", "010110", "010111", "011000", "011001", "011010", "011011", "011100", "011101", "011110", "011111", "100000", "100001", "100010", "100011", "100100", "100101", "100110", "100111", "101000", "101001", "101010", "101011", "101100", "101101", "101110", "101111", "110000", "110001", "110010", "110011", "110100", "110101", "110110", "110111", "111000", "111001", "111010", "111011", "111100", "111101", "111110", "111111"];
PDsymbols:=["t"];
skel_PD:=Skeleton(PD);
DisplayHolonomyComponents(skel_PD);
#subduction chain
Splash(DotSubductionEquivalencePoset(skel_PD));
dot_PD:=DotSkeleton(skel_PD,rec(states:=PDstates,symbols:=PDsymbols));
Splash(dot_PD);
d_label:=DotSemigroupActionWithNames(PD,[1..64],OnPoints,PDstates,PDsymbols);
Splash(d_label);
PD_Coordinatized:=HolonomyCascadeSemigroup(PD);
SplashList(DotRepHolonomyGroups(skel_PD, rec(states:=PDstates,symbols:=PDsymbols)));
SplashList(DotNaturalSubsystems(skel_PD, rec(states:=PDstates,symbols:=PDsymbols)));
import networkx as nx
from itertools import product
import sys
import numpy as np
import matplotlib.pyplot as plt
def play(G,node,nb,b):
if (G.node[node]['strategy']==0 and G.node[nb]['strategy']==0):
return 1
elif (G.node[node]['strategy']==1 and G.node[nb]['strategy']==0):
return 0
elif (G.node[node]['strategy']==0 and G.node[nb]['strategy']==1):
return b
elif (G.node[node]['strategy']==1 and G.node[nb]['strategy']==1):
return 3
def imitate(G,node):
original=G.node[node]['payoff']
choice=original
sList=[G.node[node]['strategy']]
for nb in G.neighbors(node):
if (G.node[nb]['payoff']>original and G.node[nb]['payoff']>choice):
choice=G.node[nb]['payoff']
sList=[G.node[nb]['strategy']]
elif (G.node[nb]['payoff']==choice and G.node[nb]['payoff']>original):
sList.append(G.node[nb]['strategy'])
if len(sList)==0:
return original
if len(sList)==1:
return sList[0]
elif len(sList)>1:
if 1 in sList:
return 1
else: return 0
def tAction(G):
for node in G.nodes():
for nb in G.neighbors(node):
G.node[node]['payoff']+=play(G,node,nb,b)
for node in G.nodes():
G.node[node]['next']=imitate(G,node)
for node in G.nodes():
G.node[node]['strategy']=G.node[node]['next']
def dAction(G,node):
G.node[node]['strategy']=0
def cAction(G,node):
G.node[node]['strategy']=1
N=2
M=3
G=nx.grid_graph(dim=[N,M],periodic=True)
states=list(product([0,1],repeat=N*M))
bList=[4.5,4,3.5,3]
regList=["A","B","C","D"]
for k,b in enumerate(bList):
tMap={}
dMap=[dict() for x in range(N*M)]
cMap=[dict() for x in range(N*M)]
for x in range(len(states)):
strategies={}
clear={}
i=0
for node in G.nodes():
strategies[node]=states[x][i]
clear[node]=0
i+=1
nx.set_node_attributes(G, strategies, 'strategy')
nx.set_node_attributes(G, clear, 'next')
nx.set_node_attributes(G, clear, 'payoff')
tAction(G)
for node in G.nodes():
strategies[node]=G.node[node]['strategy']
for y in range(len(states)):
if tuple(strategies.values())==states[y]:
tMap[x+1]=y
i=0
for nodeSwitch in G.nodes():
for x in range(len(states)):
strategies={}
clear={}
j=0
for node in G.nodes():
strategies[node]=states[x][j]
j+=1
nx.set_node_attributes(G, strategies, 'strategy')
dAction(G,nodeSwitch)
for node in G.nodes():
strategies[node]=G.node[node]['strategy']
for y in range(len(states)):
if tuple(strategies.values())==states[y]:
dMap[i][x]=y
i+=1
i=0
for nodeSwitch in G.nodes():
for x in range(len(states)):
strategies={}
clear={}
j=0
for node in G.nodes():
strategies[node]=states[x][j]
j+=1
nx.set_node_attributes(G, strategies, 'strategy')
cAction(G,nodeSwitch)
for node in G.nodes():
strategies[node]=G.node[node]['strategy']
for y in range(len(states)):
if tuple(strategies.values())==states[y]:
cMap[i][x]=y
i+=1
with open('PDsemi'+regList[k]+'.g','w') as f:
f.write('LoadPackage("SgpDec");\n')
for elem in tMap:
tMap[elem]+=1
f.write("t:=Transformation("+str(list(tMap.values()))+");\n")
for i in range(len(dMap)):
for elem in dMap[i]:
dMap[i][elem]+=1
f.write("d"+str(i+1)+":=Transformation("+str(list(dMap[i].values()))+");\n")
for i in range(len(cMap)):
for elem in cMap[i]:
cMap[i][elem]+=1
f.write("c"+str(i+1)+":=Transformation("+str(list(cMap[i].values()))+");\n")
print('PDstates:=[', end='')
for i in range(len(states)):
print('"', end='')
for elem in states[i]:
print(elem, end='')
print('"', end='')
if(i<len(states)-1):
print(', ', end='')
else:
print('];')
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