#Ok to post homework
#Lucy Martinez, 02-13-22, Assignment 7
restart: read `C7.txt`:
#-----My Old code:
PureNashEqui:=proc(G) local i,j,S:
S:={}:
for i from 1 to nops(G) do
for j from 1 to nops(G[1]) do
 if i in BR1(G,j) and j in BR2(G,i) then
  S:=S union {[i,j]};
 else
  S:=S;
 fi;
od:
od:
S:
end proc:
#----------------------Problem 2-----------------------#
# Write a procedure TypeCounts22(K1,K2)
# that inputs a very large positive integer (at least ten million, otherwise there may be some Maple issues, 
# the current code for MNE22(G) does not address some pathological cases, but if you make K1 large enough it
# should not be a problem), and fairly large positive integer K2 (say, around 10000), 
# uses RG(2,2,K1) K2 times and outputs the following list of length 4 of floating-point numbers
# evalf(
#[Number of Games with Exactly One Pure Nash Equilibrium , 
# Number of Games with Exactly Two Pure Nash Equilibrium and No Mixed one , 
# Number of Games with No Pure Nash Equilibrium and one Mixed,
# Number of Games with Two Pure and One Mixed] /K2)

TypeCounts22:=proc(K1,K2) local L, G, i, P, M:
L:=[0,0,0,0]:
for i from 1 to K2 do
 G:=RG(2,2,K1):
 P:=PureNashEqui(G);
 M:=MNE22(G);
 if nops(P)=1 then
  L[1]:=L[1]+1:
 fi:
 if nops(P)=2 and nops(M)=2 then
  L[2]:=L[2]+1:
 fi:
 if nops(M)=1 and nops(P)=0 then
  L[3]:=L[3]+1:
 fi:
 if nops(M)=3 and nops(P)=2 then
  L[4]:=L[4]+1:
 fi:
od:
for i from 1 to 4 do
 L[i]:=L[i]/K2:
od:
evalf[5](L):
end:

TypeCounts22(100000000,10000);
#                [0.7522, 0., 0.1281, 0.1197]


TypeCounts22(100000000,10000);
#                [0.7490, 0., 0.1201, 0.1309]


TypeCounts22(100000000,10000);
#                [0.7498, 0., 0.1265, 0.1237]


TypeCounts22(100000000,10000);
#                [0.7519, 0., 0.1207, 0.1274]


TypeCounts22(100000000,10000);
#                [0.7418, 0., 0.1298, 0.1284]


#----------------------Problem 5-----------------------#
# Generalize procedure PayOffG(G,p1,p2)
# To write a procedure PayOffGG(G,p1,p2)
# where G is an arbitrary 2-person game, with say, m (=nops(G)) strategies for Player Row, 
# and n (=nops(G[1]) strategies for Player Column, and p1, p2, are probability vectors 
# (i.e. they add up to 1) and outputs a list of length 2 with the payoffs of Player Row and Player Col.
# Note: You should check that they add-up to 1, and return FAIL if they don't,

PayOffGG:=proc(G,p1,p2) local S1,S2,i,j,L:
S1:=0:
S2:=0:
L:=[0,0]:
for i from 1 to nops(p1) do
 S1:=S1+p1[i]:
od:
for j from 1 to nops(p2) do
 S2:=S2+p2[j]:
od:
if S1=1 and S2=1 then
 for i from 1 to nops(p1) do
 for j from 1 to nops(p2) do
  L[1]:=L[1]+(p1[i]*p2[j]*G[i,j,1]):
  L[2]:=L[2]+(p1[i]*p2[j]*G[i,j,2]):
 od:
 od:
else
 RETURN(FAIL):
fi:
L: 
end: