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By Susan T. Fiske

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Assuming naively that one’s opponent is equally likely to play rock, or paper, or scissors, the greater value of winning with paper should lead all players to select paper deterministically on each round. What VonNeumann recognized was that this assumption about the behavior of one’s opponent simply could not be correct. A competitor who simply selected scissors could reliably defeat any player who actually behaved in accord with this strategy. Game theory, as developed by VonNeumann & Morgenstern (1944), addresses this limitation of classical utility theory by making the assumption that both players are aware that they face an intelligent opponent who can anticipate their actions and that both players will shape their behavior accordingly to minimize losses and maximize gains.

Perhaps surprisingly, even under these conditions the activity of the neurons varied from trial to trial. The precise number of action potentials generated and the precise pattern of action potential generation differed in an apparently random manner from trial to trial, even when the visual stimulus that the animal was evaluating was identical. 18 Nov 2004 10:44 Annu. Rev. Psychol. 56:25-56. org by Ball State University on 01/05/09. For personal use only. sgm LaTeX2e(2002/01/18) P1: IKH GLIMCHER Britten and colleagues also found that the perceptual judgments of the animals were unpredictable on these trials.

Winning with paper yields twice as much money as winning with rock or scissors, but deterministically playing paper leads to certain defeat. What VonNeumann & Morgenstern showed was that under these conditions we can predict that a rational player will titrate risk against gain and play paper two-thirds of the time, scissors one-sixth of the time, and rock one-sixth of the time. Critically, however, he must avoid making his twothirds, one-sixth, one-sixth selections in a determinate fashion; for example, in a repeated version of the game by playing paper, then scissors, then paper, then rock, then paper, and then paper.

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