#OK to post
#Rebecca Embar, 2-8-2022, Homework 6

read `C6.txt`:

#1
testgame := proc() local G,i,j,p1,p2,payoff:
	G:=RG(2,2,1000);
	print(G):
	for i from 1 to 3 do
		p1:=rand(0..100)()/100:
		p2:=rand(0..100)()/100:
		print(p1,p2):
		for j from 1 to 5 do
			print(SimulateMG(G,p1,p2,10000)):
		od:
		payoff := PayOffG(G,p1,p2):
		print(evalf(payoff)):
	od:
end:
#RESULTS

#First game
#G := [[[933, 496], [300, 242]], [[271, 112], [500, 860]]]
#p1 := 9/100, p2 := 7/10
#SimulateMG results
#[374.5375000, 344.8106000]
#[379.2939000, 349.6838000]
#[375.5151000, 341.5912000]
#[376.2373000, 346.6706000]
#[376.8238000, 345.4926000]
#PayoffG results: [376.0060000, 343.9060000]
#p1 := 59/100, p2 := 53/100
#SimulateMG results
#[529.0202000, 411.9032000]
#[528.0772000, 409.9782000]
#[529.8955000, 414.1250000]
#[526.9886000, 416.0566000]
#[528.7303000, 414.3704000]
#PayoffG results: [530.1774000, 412.2654000]
#p1 := 67/100, p2 := 1/100
#SimulateMG results
#[367.2382000, 439.9396000]
#[368.6685000, 441.4578000]
#[367.7500000, 441.1322000]
#[369.4338000, 444.9978000]
#[369.4050000, 442.8826000]
#PayoffG results: [369.4854000, 445.1734000]

#Second game
#G := [[[715, 614], [309, 142]], [[382, 555], [347, 670]]]
#p1 := 59/100, p2 := 24/25
#SimulateMG results
#[565.1518000, 579.6364000]
#[569.0752000, 581.8106000]
#[570.2661000, 580.4711000]
#[565.4986000, 580.0918000]
#[570.5954000, 581.2604000]
#PayoffG results: [568.3144000, 580.5568000]
#p1 := 19/20, p2 := 16/25
#SimulateMG results
#[557.2054000, 449.7042000]
#[558.9980000, 451.5190000]
#[559.6601000, 454.1179000]
#[560.6701000, 452.7767000]
#[557.2689000, 450.5749000]
#PayoffG results: [558.8680000, 451.6960000]
#p1 := 11/100, p2 := 1/20
#SimulateMG results
#[346.9993000, 610.8215000]
#[346.4851000, 606.2741000]
#[346.9782000, 609.5546000]
#[347.2125000, 606.7389000]
#[347.1059000, 611.5811000]
#PayoffG results: [346.6105000, 609.3985000]

#Third game
#G := [[[368, 685], [480, 427]], [[396, 3], [677, 429]]]
#p1 := 81/100, p2 := 83/100
#SimulateMG results
#[396.7711000, 536.1516000]
#[397.9837000, 537.3192000]
#[397.0134000, 536.7094000]
#[397.4420000, 531.4290000]
#[397.4164000, 536.5544000]
#PayoffG results: [397.8187000, 533.6532000]
#p1 := 29/100, p2 := 17/100
#SimulateMG results
#[582.3419000, 391.7284000]
#[579.0861000, 388.7776000]
#[579.2854000, 388.5464000]
#[580.4231000, 389.3206000]
#[579.9926000, 390.1166000]
#PayoffG results: [580.4317000, 389.7212000]
#p1 := 21/25, p2 := 37/100
#SimulateMG results
#[460.1561000, 482.1906000]
#[459.6234000, 485.3834000]
#[459.2087000, 482.9702000]
#[458.7625000, 484.9420000]
#[460.0514000, 484.1534000]
#PayoffG results: [460.0752000, 482.2872000]

#Fourth game
#G := [[[658, 235], [183, 542]], [[35, 498], [306, 612]]]
#p1 := 59/100, p2 := 29/50
#SimulateMG results
#[332.5253000, 437.7920000]
#[328.3918000, 439.8538000]
#[331.1129000, 439.2826000]
#[329.0682000, 439.9640000]
#[327.4461000, 440.6678000]
#PayoffG results: [331.5312000, 438.5354000]
#p1 := 16/25, p2 := 7/50
#SimulateMG results
#[256.4660000, 534.8960000]
#[256.8322000, 532.3813000]
#[257.9431000, 533.2326000]
#[258.2428000, 533.2167000]
#[258.4144000, 532.3204000]
#PayoffG results: [256.1816000, 533.9472000]
#p1 := 67/100, p2 := 47/100
#SimulateMG results
#[329.9286000, 452.3630000]
#[331.3161000, 449.6802000]
#[333.6836000, 448.4982000]
#[333.6477000, 447.2855000]
#[333.4242000, 449.7255000]
#PayoffG results: [331.1354000, 450.7443000]

#Fifth game
#G := [[[716, 512], [681, 421]], [[3, 738], [49, 303]]]
#p1 := 23/100, p2 := 1/20
#SimulateMG results
#[193.8125000, 347.9056000]
#[195.4834000, 348.3676000]
#[191.1887000, 347.0736000]
#[192.7499000, 347.5277000]
#[191.6892000, 348.0837000]
#PayoffG results: [192.9915000, 347.9340000]
#p1 := 3/10, p2 := 69/100
#SimulateMG results
#[226.7547000, 567.1548000]
#[228.8640000, 564.3337000]
#[222.6189000, 566.1630000]
#[223.3816000, 568.9501000]
#[227.4324000, 568.2235000]
#PayoffG results: [223.6270000, 567.3420000]
#p1 := 23/100, p2 := 39/50
#SimulateMG results
#[169.1551000, 609.3469000]
#[167.2128000, 607.8881000]
#[173.5829000, 608.4774000]
#[169.7790000, 610.1648000]
#[170.6424000, 605.0473000]
#PayoffG results: [173.0114000, 607.7264000]

#3
TragedyOfTheCommons:= proc(v,G,c,n) local vdiff:
	vdiff := diff(v,G):
	return fsolve(v+(1/n)*G*vdiff-c,G):
end:
#v(G):=sqrt(1-G)
#0.4108027069, 0.5240408206, 0.5790991062, 0.6120715420, 0.6341606640, 0.6500444109, 0.6620396765, 0.6714307918, 0.6789893673, 0.6852079369
#v(G):=(1-G)^(1/4)
#0.5980909164, 0.7159713145, 0.7695811633, 0.8009276122, 0.8217454810, 0.8366883478, 0.8479928247, 0.8568756419, 0.8640589838, 0.8700002405
#v(G):=(1-G)^(3/4)
#0.3111336476, 0.4083516515, 0.4565628023, 0.4855049838, 0.5048474518, 0.5187020389, 0.5291205867, 0.5372433987, 0.5437555690, 0.5490938253