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