#OK to post homework
#Lucy Martinez, 02-13-22, Assignment 6
restart: read `C6.txt`:
#----------------------Problem 1-----------------------#
#Using procedure RG(a,b,K) of Lecture 5 (also contained in C6.txt ), Create five random games with a=2, b=2, 
# K= 1000, and for each of these games, pick three random choices of p1 and p2 and run SimulateMG(G,p1,p2,K) 
# with K=10000, each five times. Make sure that you get similar-looking answers, and compare them to 
# the output of evalf(PayOffG(G,p1,p2))

# Game 1:
G1:=RG(2,2,1000);
#   G1 := [[[954, 299], [99, 549]], [[196, 282], [351, 16]]]

SimulateMG(G1,1/7,1/7,10000);
#                 [313.5553000, 118.4685000]

SimulateMG(G1,1/7,1/7,10000);
#                 [315.8190000, 117.0373000]

SimulateMG(G1,1/7,1/7,10000);
#                 [310.0414000, 125.0955000]

SimulateMG(G1,1/7,1/7,10000);
#                 [315.3049000, 118.8309000]

SimulateMG(G1,1/7,1/7,10000);
#                 [312.3834000, 121.2168000]

evalf(PayOffG(G1,1/7,1/7));
#                 [501.9183673, 450.4693878]


# Game 2:
G2:=RG(2,2,1000);
#   G2 := [[[478, 582], [374, 846]], [[651, 473], [693, 949]]]


SimulateMG(G2,1/12,0.65,10000);
#                [665.9169000, 940.2553000]

SimulateMG(G2,1/12,0.65,10000);
#                [667.7671000, 940.8527000]

SimulateMG(G2,1/12,0.65,10000);
#                [666.8101000, 940.5437000]

SimulateMG(G2,1/12,0.65,10000);
#                [665.9488000, 940.2656000]


SimulateMG(G2,1/12,0.65,10000);
#                [666.8101000, 940.5437000]


evalf(PayOffG(G2,1/12,0.65));
#                [647.0250000, 642.5000000]


# Game 3:
G3:=RG(2,2,1000);
#  G3 := [[[498, 630], [921, 718]], [[603, 972], [611, 128]]]


SimulateMG(G3,7/12,1/3,10000);
#                [706.4345000, 570.1080000]

SimulateMG(G3,7/12,1/3,10000);
#                [705.4760000, 571.0272000]

SimulateMG(G3,7/12,1/3,10000);
#                [708.4892000, 571.1714000]

SimulateMG(G3,7/12,1/3,10000);
#                [709.5210000, 577.8034000]

SimulateMG(G3,7/12,1/3,10000);
#                [712.0313000, 575.4334000]

evalf(PayOffG(G3,7/12,1/3));
#                [708.4722222, 572.2777778]


# Game 4:
G4:=RG(2,2,1000);
#   G4 := [[[949, 205], [863, 730]], [[470, 961], [694, 648]]]


SimulateMG(G4,1/5,2/7,10000);
#                [681.1969000, 705.8397000]

SimulateMG(G4,1/5,2/7,10000);
#                [681.5089000, 708.1801000]

SimulateMG(G4,1/5,2/7,10000);
#                [683.7733000, 704.7270000]

SimulateMG(G4,1/5,2/7,10000);
#                [682.1247000, 704.7573000]

SimulateMG(G4,1/5,2/7,10000);
#                [681.2981000, 705.3629000]

evalf(PayOffG(G4,1/5,2/7));
#                [681.5142857, 705.9428571]


# Game 5:
G5:=RG(2,2,1000);
#   G5 := [[[890, 818], [873, 769]], [[778, 548], [364, 447]]]


SimulateMG(G5,4/9,5/7,10000);
#                [759.2406000, 644.3612000]

SimulateMG(G5,4/9,5/7,10000);
#                [762.4147000, 647.8939000]

SimulateMG(G5,4/9,5/7,10000);
#                [760.8064000, 647.3895000]

SimulateMG(G5,4/9,5/7,10000);
#                [760.4020000, 646.6308000]

SimulateMG(G5,4/9,5/7,10000);
#                [760.4827000, 646.1005000]

evalf(PayOffG(G4,4/9,5/7));
#                [707.5238095, 641.9841270]


#----------------------Problem 3-----------------------#

TragedyOfTheCommons:=proc(v,G,c,n) local deriv, sol:
sol:=solve(v-c+(G/n)*diff(v,G)=0,G):
sol:
end:

seq(TagedyOfTheCommons(sqrt(1-G),G,0.5,n),n=1..10);
# 0.4108027069, 0.5240408206, 0.5790991062, 0.6120715420, 0.6341606640, 0.6500444109, 0.6620396765, 0.6714307918, 0.6789893673, 0.6852079369


seq(TagedyOfTheCommons((1-G)^(1/4),G,0.5,n),n=1..10);
# 0.5980909164, 0.7159713145, 0.7695811633, 0.8009276122, 0.8217454810, 0.8366883478, 0.8479928247, 0.8568756419, 0.8640589838, 0.8700002405


seq(TagedyOfTheCommons((1-G)^(3/4),G,0.5,n),n=1..10);
# 0.3111336476, 0.4083516515, 0.4565628023, 0.4855049838, 0.5048474518, 0.5187020389, 0.5291205867, 0.5372433987, 0.5437555690, 0.5490938253