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IAI Actuarial Core Principles · Business Economics · Pricing strategies in the financial services sector

Two insurers, A and B, each choose to keep premiums High or cut to Low. Annual profits (₹ crore, A first, B second) are: both High (50, 50); A High, B Low (20, 70); A Low, B High (70, 20); both Low (30, 30). The game is played once and the firms cannot communicate. What is the Nash equilibrium?

The Nash equilibrium is both firms choosing Low, with profits of 30 each. Low is a dominant strategy for each firm whatever the rival does, even though both High would give 50 each. This is a prisoner's dilemma outcome.

  1. ABoth High, giving (50, 50)
  2. BA High and B Low, giving (20, 70)
  3. CA Low and B High, giving (70, 20)
  4. DBoth Low, giving (30, 30)Correct
  5. There is no Nash equilibrium in pure strategies

Explanation

If B plays High, A earns 50 with High and 70 with Low, so Low is better. If B plays Low, A earns 20 with High and 30 with Low, so Low is better. Low is dominant for A and, by symmetry, for B. The equilibrium is (Low, Low) with (30, 30), although both would be better off at (High, High), the prisoner's dilemma. Both High is not stable because each has an incentive to deviate.

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