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
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
.
Examples
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Rock, paper, scissors
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Penney's game
*
Intransitive dice
A set of dice is intransitive (or nontransitive) if it contains three dice, ''A'', ''B'', and ''C'', with the property that ''A'' rolls higher than ''B'' more than half the time, and ''B'' rolls higher than ''C'' more than half the time, but it is ...
*
Street Fighter
, commonly abbreviated as ''SF'' or スト (''Suto''), is a Japanese media franchise centered on a series of fighting video and arcade games developed and published by Capcom. The first game in the series was released in 1987, followed by six ...
. 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
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Stochastic transitivity
References
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Game theory game classes
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