An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C. The terms "transitive game" or "intransitive game" are not used in game theory.

Contents

• Examples
• See also
• References

A prototypical example of an intransitive game is the game rock, paper, scissors. In probabilistic games like Penney's game, the violation of transitivity results in a more subtle way, and is often presented as a probability paradox.

Examples

• Rock, paper, scissors
• Penney's game
• Intransitive dice

See also

• Stochastic transitivity

References

• Gardner, Martin (2001). The Colossal Book of Mathematics. New York: W.W. Norton. ISBN   0-393-02023-1 . Retrieved 15 March 2013.

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