#OK to post homework 
#Lucy Martinez, 01-30-22, Assignment 2 
restart:read `C2.txt`: 
read `C3.txt`: 
#######Problem 2:#######
# Random Game 1:
G1:=Rand2PlayerGame(3,3,2);
BR1v(G1[1]);
                              [{2}, {1, 3}, {2}]

BR2v(G1[1]);
                               [{1}, {1}, {3}]

#Random Game 2:
G2:=Rand2PlayerGame(3,3,2);
BR1v(G2[1]);
                               [{1}, {2}, {2}]

BR2v(G2[1]);
                               [{3}, {1}, {1}]

#Random Game 3: 
G3:=Rand2PlayerGame(3,3,2);
BR1v(G3[1]);
                            [{1, 2, 3}, {1}, {2}]

BR2v(G3[1]);
                            [{1, 3}, {1, 2}, {2}]

#Random Game 4: 
G4:=Rand2PlayerGame(3,3,2);
BR1v(G4[1]);
                               [{3}, {3}, {2}]

BR2v(G4[1]);
                           [{2, 3}, {1, 2, 3}, {1}]

#Random Game 5: 
G5:=Rand2PlayerGame(3,3,2);
BR1v(G5[1]);
                           [{1}, {1, 2}, {1, 2, 3}]

BR2v(G5[1]);
                               [{3}, {1}, {1}]

#######Problem 4:#######
IsNash:=proc(G,a1,a2)
 if a1 in BR1(G,a2) and a2 in BR2(G,a1) then
  RETURN(true); 
 else RETURN(false); 
 fi;
end proc:

#######Problem 5:#######
##This prints out the set of nash equilibria of the given matrix
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 {G[i][j]};
 else S:=S;
 fi;
od:
od:
S:
end proc:
#Generate 5 random 2-player games where Player Row has 10 strategies, and Player Column has 12 strategies, and for each find their set of (pure) Nash Equilibria
#Random Game 1:
G6:=Rand2PlayerGame(10,12,3);
PureNashEqui(G6[1]);


                               {[2, 2], [3, 3]}

#Random Game 2: 
G7:=Rand2PlayerGame(10,12,4); 
PureNashEqui(G7[1]);


                                   {[4, 4]}

#Random Game 3: 
G8:=Rand2PlayerGame(10,12,4);
PureNashEqui(G8[1]);


                           {[3, 4], [4, 3], [4, 4]}

#Random Game 4:
G9:=Rand2PlayerGame(10,12,2);
PureNashEqui(G9[1]);


                               {[1, 2], [2, 2]}

#Random Game 5: 
G10:=Rand2PlayerGame(10,10,3);
PureNashEqui(G10[1]);


                               {[2, 3], [3, 3]}