Intransitive game

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.

Examples[]

Rock, paper, scissors
Penney's game
Intransitive dice
Street Fighter. 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.

References[]

Gardner, Martin (2001). The Colossal Book of Mathematics. New York: W.W. Norton. ISBN 0-393-02023-1. Retrieved 15 March 2013.

v t Topics in game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Game description language Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game
Equilibrium concepts	Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Perfect Bayesian equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand
Strategies	Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy Bid shading
Classes of games	Bargaining problem Cheap talk Global game Intransitive game Mean-field game Mechanism design n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Stackelberg competition Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers Tic-tac-toe Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Purification theorem Revelation principle Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Miscellaneous	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory First-move advantage in chess Game Description Language Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions

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Intransitive game

Examples[]

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References[]