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CMA Final · Strategic Cost Management · Game Theory

Two rival firms, P and Q, each choose a High price or a Low price. Profits (₹ crore) as (P, Q): both High = (10, 10); P High and Q Low = (4, 14); P Low and Q High = (14, 4); both Low = (7, 7). Assuming each acts independently and simultaneously, which outcome is the Nash equilibrium?

Both firms choosing the Low price is the Nash equilibrium. Low is the dominant strategy for each firm, since it earns more whether the rival prices High or Low. Both High gives higher joint profit but is unstable because each firm gains by cutting its price.

  1. ABoth choose Low priceCorrect
  2. BBoth choose High price
  3. CP chooses High and Q chooses Low
  4. DP chooses Low and Q chooses High

Explanation

If Q plays High, P earns 10 with High and 14 with Low, so P prefers Low. If Q plays Low, P earns 4 with High and 7 with Low, so P prefers Low. The game is symmetric, so Q also prefers Low whatever P does. Low is a dominant strategy for both firms, giving (Low, Low) with profits of 7 each. Both High looks better jointly but either firm gains by deviating, so it is not an equilibrium.

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