In
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
, 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
Rock paper scissors (also known by other orderings of the three items, with "rock" sometimes being called "stone," or as Rochambeau, roshambo, or ro-sham-bo) is a hand game originating in China, usually played between two people, in which each p ...
which is explicitly constructed as a non-transitive game. In
probabilistic
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
games like
Penney's game
Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. Player A selects a sequence of heads and tails (of length 3 or larger), and shows this sequence to player B. Player B then ...
, 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
*
Rock, paper, scissors
Rock paper scissors (also known by other orderings of the three items, with "rock" sometimes being called "stone," or as Rochambeau, roshambo, or ro-sham-bo) is a hand game originating in China, usually played between two people, in which each p ...
*
Penney's game
Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. Player A selects a sequence of heads and tails (of length 3 or larger), and shows this sequence to player B. Player B then ...
*
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
''Halo Wars 2'' is a real-time strategy video game developed by 343 Industries and Creative Assembly. It was published by Microsoft Studios and released in February 2017 on Windows and Xbox One. The game is set in the science fiction universe ...
. A videogame noted for having a cycle in which aircraft beat landcraft, landcraft beat infantry, and infantry beat aircraft.
See also
*
Stochastic transitivity Stochastic transitivity models are stochastic versions of the transitivity property of binary relations studied in mathematics. Several models of stochastic transitivity exist and have been used to describe the probabilities involved in experiment ...
References
*
Game theory game classes
{{Mathapplied-stub