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IAI Actuarial Core Principles · Business Management · Decision-making process, attitude to risk and competition

Two Indian health insurers sell similar products. Each can keep premiums at the current level or cut them. Payoffs (profit in Rs crore, Insurer X first, Insurer Y second): both keep (50, 50); X cuts, Y keeps (70, 20); X keeps, Y cuts (20, 70); both cut (30, 30). The firms move simultaneously and cannot make binding agreements. What is the Nash equilibrium?

The Nash equilibrium is both insurers cutting premiums, with payoffs of 30 each. Cutting is better for each firm whichever choice the rival makes, so it is a dominant strategy, even though both keeping premiums would give each 50.

  1. ABoth keep premiums, giving (50, 50)
  2. BBoth cut premiums, giving (30, 30)Correct
  3. CX cuts and Y keeps, giving (70, 20)
  4. DX keeps and Y cuts, giving (20, 70)
  5. There is no pure-strategy Nash equilibrium

Explanation

If Y keeps, X gets 50 by keeping and 70 by cutting, so X cuts. If Y cuts, X gets 20 by keeping and 30 by cutting, so X cuts. The game is symmetric, so Y also cuts. Both keeping is not an equilibrium because each gains by deviating.

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