Intransitive game

An intransitive or non-transitive game is a term sometimes used for 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, however.

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
• Fire Emblem. The video game franchise that popularized intransitive cycles in unit weapons: Swords and Magic beats Axes and Bows, Axes and Bows beat Lances and Knives, and Lances and Knives beat Swords and magic

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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