Nontransitive game

A non-transitive game is a game for which the various strategies produce one or more "loops" of preferences. As a result, in a non-transitive game the fact that strategy A is preferred over strategy B, and strategy B is preferred over strategy C, does not necessarily imply that strategy A is preferred over strategy C. See also intransitivity, transitive relation.

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

Examples of non-transitive games are:

• Rock, Paper, Scissors
• Penney's game
• Nontransitive dice

References

• Gardner, Martin (2001). The Colossal Book of Mathematics. New York: W.W. Norton. ISBN 0393020231. 

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