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CMA Final · Strategic Cost Management · Game Theory

Two firms, X and Y, each choose a High or Low price. Payoffs are annual profits in ₹ crore, written as (X, Y). High-High: (10, 10) High-Low (X high, Y low): (4, 14) Low-High (X low, Y high): (14, 4) Low-Low: (7, 7) The firms move simultaneously without any binding agreement. What is the total industry profit at the Nash equilibrium?

Total industry profit at equilibrium is ₹14 crore. Low price is the dominant strategy for each firm whatever the rival does, so both choose Low and earn ₹7 crore each. The higher joint profit of ₹20 crore from High-High is not sustainable without an agreement.

  1. A₹20 crore
  2. B₹18 crore
  3. C₹14 croreCorrect
  4. D₹7 crore

Explanation

If Y plays High, X earns 10 with High and 14 with Low, so X prefers Low. If Y plays Low, X earns 4 with High and 7 with Low, so X again prefers Low. Low is dominant for X, and by symmetry for Y. The Nash equilibrium is Low-Low with profits (7, 7), a total of 14. The ₹20 crore total is the cooperative High-High outcome, which is not stable.

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