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.
/PDsemi.py Secret
Created
June 30, 2020 21:46
Code used to generate and analyze the prisoner's dilemma as a transformation semigroup.
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| #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))); |
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| 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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