Question: Suppose that u1: A represents the preferences of the player 1 in a two-person strictly competitive game (example 1.50). Then the function u2

Suppose that u1: A ∊ ℜ represents the preferences of the player 1 in a two-person strictly competitive game (example 1.50). Then the function
u2 = - u1 represents the preferences of the player 2 and
u1(a) + u2(a) = 0 for every a ∊ A
Consequently a strictly competitive game is typically called a zero-sum game.

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