#OK to post
#Rebecca Embar, 2-11-2022, Homework 7

#2
TypeCounts22 := proc(K1,K2) local i,G,l,purenash:
	if K1 > 10000000 then
		l := [0,0,0,0]:
		purenash := {[0,0],[1,0],[0,1],[1,1]}:
		for i from 1 to K2 do
			G := RG(2,2,K1):
			#Exactly one pure
			if nops(purenash intersect MNE22(G)) = 1 then
				l[1] := l[1]+1:
			fi:
			if nops(purenash intersect MNE22(G)) = 2 then
				#Two pure no mixed
				if nops(MNE22(G) minus purenash) = 0 then l[2] = l[2]+1 fi:
				#Two pure one mixed
				if nops(MNE22(G) minus purenash) = 1 then l[4] = l[4]+1 fi:
			fi:
			#No pure and one mixed
			if nops(purenash intersect MNE22(G)) = 0 and nops(MNE22(G)) = 1 then
				l[3] := l[3]+1:
			fi:
		end:
		return evalf(l/K2):
	fi:
	return FALSE:
end:
#I think this program works since I ran it on smaller values of K2 and it outputted
#correct-looking data, but it took too long to run for K1=10^8 and K2=10000

#3

#5
PayoffG:=proc(G,p1,p2) local x,i,j:
	if add(x,x in p1)=1 and add(x,x in p2)=1 then
		return add(x,x in seq(seq(p1[i]*p2[j]*G[i][j],j=1..nops(G[1])),i=1..nops(G)));
	fi:
	return FALSE:
end: