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. 

This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Rock-paper-scissors Applied mathematics stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР Yasmine Hanani George Johnston Look at other dictionaries: Nontransitive dice — A set of nontransitive dice is a set of dice for which the relation is more likely to roll a higher number is not transitive. See also intransitivity. This situation is similar to that in the game Rock, Paper, Scissors, in which each element has… …   Wikipedia Penney's game — (named after its inventor Walter Penney) is a binary (head/tail) sequence generating game between two players. At the start of the game, the two players agree on the length of the sequences to be generated. This length is usually taken to be… …   Wikipedia Chicken (game) — For other uses, see Chicken (disambiguation). The game of chicken, also known as the hawk dove or snowdrift[1] game, is an influential model of conflict for two players in game theory. The principle of the game is that while each player prefers… …   Wikipedia Cooperative game — This article is about a part of game theory. For video gaming, see Cooperative gameplay. For the similar feature in some board games, see cooperative board game In game theory, a cooperative game is a game where groups of players ( coalitions )… …   Wikipedia Coordination game — In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies. Coordination games are a formalization of the idea of a coordination problem, which… …   Wikipedia Dictator game — The dictator game is a game in experimental economics, similar to the ultimatum game. Experimental results offer evidence against the rationally self interested individual (sometimes called the homo economicus) concept of economic behavior,[1]… …   Wikipedia Strategy (game theory) — In game theory, a player s strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player s behaviour. A player s strategy will determine the action the player will take at any stage of the… …   Wikipedia Normal-form game — In game theory, normal form is a way of describing a game. Unlike extensive form, normal form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying… …   Wikipedia Symmetric game — In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff… …   Wikipedia Zero–sum game — For other uses, see Zero sum (disambiguation). In game theory and economic theory, a zero sum game is a mathematical representation of a situation in which a participant s gain (or loss) of utility is exactly balanced by the losses (or gains) of… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”