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IAI Actuarial Core Principles · Business Economics · Profit maximisation under imperfect competition

Two insurers in a small market each choose between keeping premiums high or cutting them. If both keep high, each earns Rs 50 crore; if both cut, each earns Rs 30 crore; if one cuts while the other stays high, the cutter earns Rs 70 crore and the other Rs 10 crore. Played once, which outcome results and why?

Both insurers cut premiums, ending with Rs 30 crore each. Cutting pays more whatever the rival does, so it is a dominant strategy, even though both would earn more by keeping premiums high; this is a prisoner's dilemma.

  1. ABoth keep premiums high, since this maximises joint profit and is a Nash equilibrium
  2. BBoth cut premiums, since cutting is a dominant strategy for each insurerCorrect
  3. COne cuts and the other stays high, since payoffs are asymmetric
  4. DBoth keep premiums high, since cutting risks the lowest payoff of Rs 10 crore
  5. No equilibrium exists in pure strategies

Explanation

If the rival stays high, cutting gives 70 against 50; if the rival cuts, cutting gives 30 against 10. Cutting is better in both cases, so it is dominant. The Nash equilibrium is both cutting with Rs 30 crore each, worse than the Rs 50 crore from mutual restraint, a prisoner's dilemma. Option A is jointly best but not stable.

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