#OK to post homework 
#Natalya Ter-Saakov, Feb 13, Assignment 6 
read "C6.txt":

#Problem 1

#Choosing strategies at random(ish) 
p:=rand(100)

#Game 1 
G1:=RG(2,2,1000):
#[[[450, 565], [189, 672]], [[180, 949], [573, 319]]] 

#Strategy 1
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G1,p1,p2,10000), i=1..5); 
evalf(PayOffG(G1,p1,p2));

#Output:
# p1 = 3/10, p2 = 23/25
# [277.2081000, 800.6475000],
# [276.4227000, 801.1964000], 
# [276.9537000, 800.4514000],
# [275.2305000, 802.4073000], 
# [278.5245000, 798.4845000]

# [276.7440000, 801.0880000]


#Strategy 2
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G1,p1,p2,10000), i=1..5);
evalf(PayOffG(G1,p1,p2));

#Output:
# p1 = 8/25, p2 = 31/50
# [336.6714000, 676.1079000],
# [338.1972000, 675.5260000], 
# [335.0694000, 677.0653000],
# [337.0560000, 674.1594000], 
# [335.1564000, 678.8668000]

# [336.2136000, 676.3392000]


#Strategy 3
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G1,p1,p2,10000), i=1..5);
evalf(PayOffG(G1,p1,p2));

#Output:
# p1 = 97/100, p2 = 13/25
# [326.8149000, 617.4450000],
# [326.6379000, 617.2751000], 
# [324.5184000, 617.7847000],
# [325.0725000, 617.9833000], 
# [326.1525000, 618.0019000]

# [326.0376000, 617.2672000]


#Game2 
G2:=RG(2,2,1000): 
#[[[631, 557], [334, 605]], [[960, 520], [573, 852]]]

##Strategy 1
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G2,p1,p2,10000), i=1..5); 
evalf(PayOffG(G2,p1,p2));

#Output:
# p1 = 17/50, p2 = 3/20
# [548.2851000, 733.8006000],
# [542.9881000, 731.9971000], 
# [545.8780000, 732.1315000],
# [546.1334000, 731.4349000], 
# [547.8156000, 732.4683000]

# [545.2000000, 732.7040000]


#Strategy 2
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G2,p1,p2,10000), i=1..5);
evalf(PayOffG(G2,p1,p2));

#Output:
# p1 = 3/25, p2 = 73/100
# [819.9317000, 602.8205000],
# [820.7318000, 604.8722000], 
# [821.0560000, 603.8228000],
# [821.2363000, 603.2084000], 
# [817.6918000, 604.8887000]

# [818.9460000, 604.8784000]


#Strategy 3
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G2,p1,p2,10000), i=1..5);
evalf(PayOffG(G2,p1,p2));

#Output:
# p1 = 39/100, p2 = 2/5
# [622.9846000, 666.1414000],
# [617.8157000, 667.2850000], 
# [619.7185000, 667.6743000],
# [621.6174000, 666.0169000], 
# [622.3780000, 665.9511000]

# [620.5500000, 667.1740000]


#Game3 
G3:=RG(2,2,1000): 
#[[[638, 318], [686, 18]], [[255, 1], [997, 426]]]

##Strategy 1
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G3,p1,p2,10000), i=1..5); 
evalf(PayOffG(G3,p1,p2));

#Output:
# p1 = 1/100, p2 = 1/25
# [967.0703000, 406.5876000],
# [965.8759000, 405.9167000], 
# [967.4700000, 406.8200000],
# [965.0955000, 405.6599000], 
# [964.7722000, 405.6753000]

# [964.4876000, 405.2100000]


#Strategy 2
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G3,p1,p2,10000), i=1..5);
evalf(PayOffG(G3,p1,p2));

#Output:
# p1 = 91/100, p2 = 41/50
# [623.0884000, 250.1473000],
# [621.6964000, 246.0511000], 
# [622.7143000, 245.4895000],
# [622.9812000, 248.4692000], 
# [622.4315000, 245.5983000]

# [623.4128000, 247.2150000]


#Strategy 3
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G3,p1,p2,10000), i=1..5);
evalf(PayOffG(G3,p1,p2));

#Output:
# p1 = 99/100, p2 = 17/20
# [642.5334000, 270.2602000],
# [642.4772000, 273.2863000], 
# [642.0064000, 270.7714000],
# [642.1765000, 270.4138000], 
# [642.7680000, 270.1332000]

# [642.4110000, 270.9175000]


#Game 4 
G4:=RG(2,2,1000):
#[[[68, 919], [135, 566]], [[60, 92], [308, 138]]]

#Strategy 1
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G4,p1,p2,10000), i=1..5); 
evalf(PayOffG(G4,p1,p2));

#Output:
# p1 = 91/100, p2 = 87/100
# [77.49180000, 801.0296000],
# [78.14470000, 805.6261000], 
# [77.32120000, 809.4618000],
# [77.53970000, 805.4234000], 
# [78.53910000, 800.9597000]

#  [78.10770000, 803.3483000]


#Strategy 2
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G4,p1,p2,10000), i=1..5);
evalf(PayOffG(G4,p1,p2));

#Output:
# p1 = 24/25, p2 = 27/50
# [101.5821000, 731.7150000],
# [102.0680000, 729.5912000], 
# [101.5732000, 731.6473000],
# [101.8374000, 730.1494000], 
# [102.5850000, 728.3742000]

# [101.8304000, 730.8816000]


#Strategy 3
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G1,p1,p2,10000), i=1..5);
evalf(PayOffG(G1,p1,p2));

#Output:
# p1 = 11/50, p2 = 63/100
# [139.3883000, 261.4931000],
# [138.8351000, 257.5121000], 
# [139.4517000, 258.1176000],
# [138.1518000, 256.0401000], 
# [140.7820000, 253.6239000]

# [138.7866000, 258.4814000]


#Game 5 
G5:=RG(2,2,1000):
#[[[468, 244], [942, 317]], [[340, 964], [759, 362]]]

#Strategy 1
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G5,p1,p2,10000), i=1..5); 
evalf(PayOffG(G5,p1,p2));

#Output:
# p1 = 41/100, p2 = 1/2
# [614.0345000, 502.8989000],
# [613.7875000, 508.2861000], 
# [611.0733000, 506.9721000],
# [609.8910000, 506.5046000], 
# [615.4251000, 499.8876000]

# [613.2550000, 506.1750000]


#Strategy 2
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G5,p1,p2,10000), i=1..5);
evalf(PayOffG(G5,p1,p2));

#Output:
# p1 = 13/100, p2 = 19/100
# [701.7713000, 453.5147000],
# [702.0214000, 454.2184000], 
# [702.0555000, 453.4058000],
# [706.0465000, 448.1712000], 
# [697.8205000, 458.2753000]

# [701.8215000, 453.8575000]


#Strategy 3
p1:=p()/100; p2:=p()/100;
seq(SimulateMG(G5,p1,p2,10000), i=1..5);
evalf(PayOffG(G5,p1,p2));

#Output:
# p1 = 2/5, p2 = 49/50
# [399.5735000, 672.1241000],
# [400.7001000, 669.6647000], 
# [398.7718000, 675.0115000],
# [399.6496000, 671.9228000], 
# [399.1630000, 673.2818000]

# [400.0200000, 669.3600000]

#All of the simulations approximate the calculated values

#Problem 2 was reading


#Problem 3

#TragedyOfTheCommons(v,G,c,n):inputs 
# (i) An expression,v, for a function that is positive in the variable G, in 0 d G d 1, but whose first and second derivatives are negative there (like in Fig. 1.2.4 in the book with G_max=1);
# (ii) a number c, the cost of buying and caring for the goat, (between 0 and 1); 
# (iii) a positive integer n, the number of farmers; 
# and outputs the Nash Equlibrium G*. 

TragedyOfTheCommons := proc(v,G,c,n):
 fsolve(v-c+G*diff(v,G)/n,G): 
end:

seq(TragedyOfTheCommons(sqrt(1-G),G,0.5,n),n=1..10);

#Output:
# 0.4108027069,
# 0.5240408206,
# 0.5790991062,
# 0.6120715420,
# 0.6341606640, 
# 0.6500444109,
# 0.6620396765,
# 0.6714307918,
# 0.6789893673,
# 0.6852079369

seq(TragedyOfTheCommons((1-G)^(1/4),G,0.5,n),n=1..10);

#Output:
# 0.5980909164,
# 0.7159713145,
# 0.7695811633,
# 0.8009276122,
# 0.8217454810, 
# 0.8366883478,
# 0.8479928247,
# 0.8568756419,
# 0.8640589838,
# 0.8700002405

seq(TragedyOfTheCommons((1-G)^(3/4),G,0.5,n),n=1..10);

#Output:
# 0.3111336476,
# 0.4083516515,
# 0.4565628023,
# 0.4855049838,
# 0.5048474518, 
# 0.5187020389,
# 0.5291205867,
# 0.5372433987,
# 0.5437555690,
# 0.5490938253

seq(TragedyOfTheCommons(sqrt(1-G),G,0.5,n),n=1..10);

#Output:
# 0.4108027069,
# 0.5240408206,
# 0.5790991062,
# 0.6120715420,
# 0.6341606640, 
# 0.6500444109,
# 0.6620396765,
# 0.6714307918,
# 0.6789893673,
# 0.6852079369

#In each case, as the number of farmers grows, so does the total number of goats, to the detriment of the social good.