# OK to post homework
# RDB, 2022-02-20, HW9

# 3.

read "C7.txt":
G := [[ [R, R], [S, T] ],
      [ [T, S], [P, P] ]]:

# Snowdrift.
eq := MNE22(G) assuming T > R and R > P and S > P:

eq := eq minus {[0, 1], [1, 0]}:
# mixed := eq[1];

Payoffs := PayOffG(G, mixed[1], mixed[2]):
# print(`The net payoff at the strictly mixed Nash equilibrium in Snowdrift is`);
# simplify(Payoffs[1] + Payoffs[2]);

# 4.

symmetric4Way := []:
mixed4Way := []:

(*
for L in permute([T, R, S, P]) do:
    res := MNE22(G) assuming L[1] > L[2] and L[2] > L[3] and L[3] > L[4]:
    symmetric4Way := [op(symmetric4Way), res]:
    mixedRes := res minus {[0, 0], [0, 1], [1, 0], [1, 1]}:
    if mixedRes <> {} then
        mixed4Way := [op(mixed4Way), L]:
    fi:
od:
*)

(*
mixed4Way:

    [[T, R, S, P], [T, S, R, P], [T, S, P, R], [R, T, P, S], [R, P, T, S],

        [R, P, S, T], [S, T, R, P], [S, T, P, R], [S, P, T, R], [P, R, T, S],

        [P, R, S, T], [P, S, R, T]]
*)


# Some observations: The mixed equilibrium (if it exists) will always be the
# same, because it comes from solving {EQ1 = 0, EQ2 = 0}, which doesn't care
# about constraints. The question is whether the underlying slopes *can* be
# zero, and if them being zero matches the other conditions.

# 5.

# This takes a long time to run! I don't have any answers yet.
# We should look into it again.

read "C9.txt":

N := 2:
M := 2:

G1 := [seq([seq([Q[i, j], Q[j, i]], j=1..M)], i=1..N)]:
vars := [seq(Q[floor((k - 1) / N) + 1, (k - 1) mod M + 1], k=1..N*M)]:

symNMWay := []:

(*
step := 0:
for L in permute(vars) do:
    cond := andseq(L[i] > L[i + 1], i=1..nops(L) - 1):
    print(step);
    print(cond);
    res := MNE2(G1) assuming cond:
    symNMWay := [op(symNMWay), res]:
    step := step + 1:
od;
*)