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The payoff value for which each player in a game always selects the same strategy is known as :

  • A.saddle point
  • B.equilibrium point
  • C.both (A) and (B)
  • D.none of the above

Answer: C

Such a payoff is called both a saddle point and an equilibrium point.

In a two-person zero-sum game with a pure-strategy solution, the payoff at the intersection of the optimal row and column is the minimum of its row and the maximum of its column. Maximin equals minimax there, neither player gains by deviating, and so each player always selects the same pure strategy.

Game theory texts call this payoff the saddle point (after the shape of the payoff surface) and also the equilibrium point (because neither player has an incentive to move). Since both names are standard, choosing only one of them is incomplete, and 'none of the above' is wrong.

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