Suppose you are one of two producers of aluminium. You (firm 1) and your competitor (firm 2) announce simultaneously the quantities Q1 and Q2 (in tonnes) and earn the profits Q1*P(Q) and Q2*P(Q), respectively, where P(Q) = 50 – Q is the market price per tonne of aluminium and Q = Q1 + Q2 is the total output. Assume, for simplicity, that there are no production costs. a) Can the collusive agreement to produce Q1 = Q2 = 12 tons of aluminium be sustained in a Nash equilibrium of the one-shot game? Explain your answer. c) Find all pure strategy Nash equilibria when both firms simultaneously announce prices from the set {0,1,…,10} instead of quantities and only the firm with the lowest price p sells 50 - p tonnes (half of this amount when both firms post the same price).
Suppose you are one of two producers of aluminium. You (firm 1) and your competitor (firm 2) announce simultaneously the quantities Q1 and Q2 (in tonnes) and earn the profits Q1*P(Q) and Q2*P(Q), respectively, where P(Q) = 50 – Q is the market
a) Can the collusive agreement to produce Q1 = Q2 = 12 tons of aluminium be sustained in a Nash equilibrium of the one-shot game? Explain your answer.
c) Find all pure strategy Nash equilibria when both firms simultaneously announce prices from the set {0,1,…,10} instead of quantities and only the firm with the lowest price p sells 50 - p tonnes (half of this amount when both firms post the same price).
d) Discuss the different models of competition in parts a and c. Which type of competition would the involved firms prefer? Which type of competition would the consumers prefer? Explain
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