CMA Final · Strategic Cost Management · Game Theory

Two rival firms, P and Q, each choose a High price or a Low price. Profits in Rs lakh (P, Q) are: both High (50, 50); P High and Q Low (20, 70); P Low and Q High (70, 20); both Low (30, 30). The firms move simultaneously and without any binding agreement. What is the Nash equilibrium outcome?

The Nash equilibrium is both firms choosing Low and each earning Rs 30 lakh. Low is a dominant strategy for each firm whatever the rival does, so the jointly better High-High outcome of Rs 50 lakh each is not stable. This is a prisoner's dilemma.

AEach firm earns Rs 30 lakh, both choosing LowCorrect
BEach firm earns Rs 50 lakh, both choosing High
CP earns Rs 70 lakh and Q earns Rs 20 lakh
DP earns Rs 20 lakh and Q earns Rs 70 lakh

Explanation

If Q chooses High, P gets 50 from High and 70 from Low, so P prefers Low. If Q chooses Low, P gets 20 from High and 30 from Low, so P again prefers Low. Low is therefore a dominant strategy for P, and by symmetry for Q. The equilibrium is (Low, Low) with 30 each. (High, High) gives 50 each but is not stable because each firm gains by cutting its price.

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Practise Game Theory Free diagnostic mock

Two rival firms, P and Q, each choose a High price or a Low price. Profits in Rs lakh (P, Q) are: both High (50, 50); P High and Q Low (20, 70); P Low and Q High (70, 20); both Low (30, 30). The firms move simultaneously and without any binding agreement. What is the Nash equilibrium outcome?

Explanation

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