# OK to post homework
# RDB, 2022-01-30, HW2

read "C2.txt":

# 1. I continue to identify as someone who knows Maple.

# 2.

(*
for k from 1 to 5 do
    G := Rand2PlayerGame(3, 3, 10)[1]:
    print(Matrix(G)):
    print(`Best responses for row player are`, BR1v(G)):
    print(`Best responses for column player are`, BR2v(G)):
od:

*)

# 3. Done!

# 4.

IsNash := (G, a1, a2) -> a1 in BR1(G, a2) and a2 in BR2(G, a1):

# 5.

PureNashEqui := proc(G)
    local row_best, col_best:
    row_best := BR1v(G):
    col_best := BR2v(G):

    equi := {}:

    for row_strat from 1 to nops(col_best) do
        col_responses := col_best[row_strat]:
        for col_response in col_responses do
            if row_strat in row_best[col_response] then
                equi := equi union {[row_strat, col_response]}:
            fi:
        od:
    od:

    for col_strat from 1 to nops(row_best) do
        row_responses := row_best[col_strat]:
        for row_response in row_responses do
            if col_strat in col_best[row_response] then
                equi := equi union {[row_response, col_strat]}:
            fi:
        od:
    od:

    equi:
end:

(*
for k from 1 to 5 do
    G := Rand2PlayerGame(10, 12, 10)[1]:
    # Maple isn't a fan of printing big matrices, and I don't remember how to change its mind.
    # print(Matrix(G)):
    print(`Nash equilibria are`, PureNashEqui(G)):
od:
*)