Because we have
said that each child will try to get the bigger piece, the
chooser??™s optimal strategy is obvious: He will choose
the larger piece. Because the cu er is also trying to
get the largest piece possible, she will try to cut the
pieces as evenly as possible. The optimal strategies
for each player meet in payo?¬? #1: The chooser gets a
slightly bigger piece.
The cake cu ing scenario is an example of a zerosum
game. By this we mean that the total amount won
at the end of the game is exactly equal to the amount
lost. In this case, the chooser gains the crumb lost by
the cu er. Because of the nature of zero-sum games,
the interests of the players are diametrically opposed.
What one player loses is gained by the other.
11.7 Cake cu ing scenario payo?¬? matrix
Improving Player Choices 321
322 Chapter 11: Fun and Accessibility
What von Neumann discovered in his study is that
there is an optimal strategy for each player in games of
this nature that will produce the best possible results in a
given situation. He called this concept ???minimax theory.???
Minimax theory states that there is a rational way
for players to make choices in a game, if we are talking
about a two-player, zero-sum game.
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