intransitive game
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.
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
References
- {{cite book |last=Gardner |first=Martin |author-link=Martin Gardner |title=The Colossal Book of Mathematics |location=New York |publisher=W.W. Norton |year=2001 |isbn=0-393-02023-1 |url=http://books.wwnorton.com/books/detail.aspx?ID=4897 |access-date=15 March 2013}}
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Category:Game theory game classes
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