Intransitive game

In game theory, an intransitive or non-transitive game is the one in which the various strategies produce one or more "loops" of preferences. In a non-transitive game in which strategy A is preferred over strategy B, and strategy B is preferred over strategy C, strategy A is not necessarily preferred over strategy C.

A prototypical example non-transitive game is the game rock, paper, scissors which is explicitly constructed as a non-transitive game. 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
• Street Fighter. The videogame franchise that introduced the common convention that block beats strike, strike beats throw, and throw beats block.
• Halo Wars 2. A videogame noted for having a cycle in which aircraft beat landcraft, landcraft beat infantry, and infantry beat aircraft.

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.