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Why does minimax coincide with equilibrium in a zero sum game?

  • A.Zero sum games always have a unique optimal strategy
  • B.Both of the players share the same evaluation of every position
  • C.Equilibrium is defined only for zero sum games
  • D.Each player's best response is to minimise the other's payoff

Answer: D

Because one player's gain is the other's loss, maximising one's own payoff is identical to minimising the opponent's, and the minimax value is exactly the equilibrium value. In non zero sum games the two diverge and cooperation becomes possible. Uniqueness, shared evaluation and definitional restriction are not the argument. That a special structure collapses two solution concepts into one explains why the general theory is needed only when that structure is absent.

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