- Source: 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
Stochastic transitivity
References
Gardner, Martin (2001). The Colossal Book of Mathematics. New York: W.W. Norton. ISBN 0-393-02023-1. Retrieved 15 March 2013.
Kata Kunci Pencarian:
- Intransitive game
- Intransitivity
- Intransitive dice
- Tic-tac-toe
- Chopsticks (hand game)
- Monty Hall problem
- Solving chess
- No-win situation
- Game balance
- Determinacy
