Question

Two cocaine producers are considering whether to form a cartel. They have two actions: either make prices high (H), or keep them low (L). If they both agree to form a cartel, agreeing to keep prices high (H), then they can make profits of $10 million each. If one producer keeps prices high (H), while the other makes them low (L), then the former makes a profit of $0, while the latter makes a profit of $15 million. If they both have low prices, then they each make $5 million. Depict this situation in a payoff matrix. What is the Nash equilibrium?

Answer 1

(a)

(b) In Nash equilibrium, each producer decides his own strategy on the basis of strategy chosen by the other producer.

When Producer 2 prices High, Producer 1 Prices Low since profit is higher ($15 million > $10 million).

When Producer 2 prices Low, Producer 1 Prices Low since profit is higher ($5 million > $0 million).

When Producer 1 prices High, Producer 2 Prices Low since profit is higher ($15 million > $10 million).

When Producer 1 prices Low, Producer 2 Prices Low since profit is higher ($5 million > $0 million).

Therefore, Nash equilibrium is: (Low price, Low price) .