Two identical firms

Two identical firms have: MC = $1 and face a market demand function of: P = 6 – Q.
Thus, total quantity, Q = q1 + q2, the sum of what each firm produces, and profit (payoff) per firm (same for both), (pi)1 = (P – MC)xq1 = [(6 – Q) – 1]xq1 = [5 – (q1 + q2)]=q1

a) Cournot Duopoly: Each firm chooses a discrete quantity: 0, 1, 2, or 3. Present the game
in matrix form, and find its pure strategy Nash equilibria. Are there any dominant or
dominated strategies for either player?
b) Bertrand Duopoly: Each firm can choose any price. What is/are the Nash equilibrium/a?