#OK to post homework 
#Natalya Ter-Saakov, Jan 30, 2022, Assignment 2 

read "C2.txt";

#Print first random matrix
G1:= Rand2PlayerGame(2,3,7):matrix(G1[1]);

BR1v(G1[1]);
#The best response list for Player Row is [{2}, {1}, {1}].

BR2v(G1[1]);
#The best response list for Player Column is [{3}, {3}].

#Print second random matrix
G2:= Rand2PlayerGame(5,5,20): matrix(G2[1]);

BR1v(G2[1]);BR2v(G2[1]);
#The best response list for Player Row is [{4}, {4}, {5}, {1}, {5}]
#The best response list for Player Column is [{3}, {1}, {5}, {3}, {3}]

#Print third random matrix
G3:= Rand2PlayerGame(3,3,3): matrix(G3[1]);

BR1v(G3[1]);BR2v(G3[1]);
#The best response list for Player Row is [{1, 2, 3}, {1, 3}, {2}]
#The best response list for Player Column is [{1}, {1}, {1, 3}]

#Print fourth random matrix
G4:= Rand2PlayerGame(3,3,100): matrix(G4[1]);

BR1v(G4[1]);BR2v(G4[1]);
#The best response list for Player Row is [{1}, {3}, {3}]
#The best response list for Player Column is [{2}, {2}, {3}]

#Print fifth random matrix
G5:= Rand2PlayerGame(6,6,100): matrix(G5[1]);

BR1v(G5[1]);BR2v(G5[1]);
#The best response list for Player Row is [{5}, {5}, {4}, {2}, {2}, {5}]
#The best response list for Player Column is [{4}, {1}, {1}, {6}, {6}, {2}]

#IsNash(G,a1,a2): inputs a 2-player game bi-matrix G, and members a1,a2 of A1, A2 respectively (that in our convention are integers from {1, ..., nops(G)} and {1, ..., nops(G[1])}) and outputs true or false according to whether [a1,a2] is a Nash Equilibrium. 
IsNash:= proc(G,a1, a2):
if a1 in BR1(G,a2) and a2 in BR2(G,a1) then: 
return true 
fi: 
false: 
end:

#PureNashEqui(G): inputs a bi-matrix G, and outputs the (possibly) emtpy set of pairs [a1,a2] that are (pure) Nash Equilibria. 
PureNashEqui:=proc(G) local a1,a2,nash: 
nash:={}: 
for a1 from 1 to nops(G) do:
 for a2 from 1 to nops(G[1]) do: 
  if IsNash(G,a1,a2) then: 
   nash := nash union {[a1,a2]}: 
  fi: 
 od: 
od: 
nash:
end:


PureNashEqui(GameDB(1)[1][1]);
#This correctly identifies the Nash equilibrium of 'Prisoner's Dilemma': {[2, 2]}

matrix(GameDB(1)[2][1]);
PureNashEqui(GameDB(1)[2][1]);
#This correctly identifies the Nash equilibria of 'Battle of the sexes':{[1, 1], [2, 2]}

GN1:=Rand2PlayerGame(10,12,20): 
matrix(GN1[1]): 
PureNashEqui(GN1[1]);
#                                   {[7, 9]}

GN2:=Rand2PlayerGame(10,12,20): 
matrix(GN2[1]): 
PureNashEqui(GN2[1]);
#                          {[1, 12], [4, 3], [5, 4]}

GN3:=Rand2PlayerGame(10,12,20): 
matrix(GN3[1]): 
PureNashEqui(GN3[1]);
#                      {[1, 5], [4, 10], [8, 11], [9, 8]}

GN4:=Rand2PlayerGame(10,12,20): 
matrix(GN4[1]): 
PureNashEqui(GN4[1]);
#                                   {[1, 6]}

GN5:=Rand2PlayerGame(10,12,20): 
matrix(GN5[1]): 
PureNashEqui(GN5[1]);
#                  {[2, 6], [5, 8], [7, 2], [9, 11], [10, 7]}