Identical firms

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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) x q1 = [(6 – Q) – 1] x q1 = [5 – (q1 + q2)] x 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?