This paper considers a game between two players who choose from a collection of objects. The players make their choices alternately and Vi,j represents the value or amount that the ith player will gain if he selects the jth object. In relation to these values, the players may have various strategies or approaches to the game, and each of them constitutes a distinct theoretical problem. The paper formulates and solves three of these problems, each one having practical significance (for example, for the draft of professional football players).

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