Talk:Intransitive game

Requested move 11 April 2021

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: Weak consensus to move to Intransitive game. Notwithstanding BarrelProof remark, my own quick research also shows that "intransitive game" is somewhat more common, and it would be nice to have consistency with Intransitivity and Intransitive dice. No such user (talk) 11:11, 13 May 2021 (UTC)

Nontransitive game → Intransitive game – The term "intransitive" is more commonly used than "nontransitive" according to Google Ngram Viewer, which is likely to make "intransitive" sound more natural. Additionally, the article on the main topic is located at Intransitivity. I do think the current title is also recognizable, precise, and concise, making this move not urgent. Ilzolende (talk) 01:31, 11 April 2021 (UTC) —Relisted. 2pou (talk) 18:23, 21 April 2021 (UTC) The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Comment: The fact that the "intransitive" is more a common word than "nontranstitive", completely outside of this context, seems pretty irrelevant, especially since the most common meaning of "intransitive" is in the context of grammar rather than mathematics or game theory. —&#8239;BarrelProof (talk) 01:42, 12 April 2021 (UTC)
 * Support to be WP:CONSISTENT with the main article located at Intransitivity. Rreagan007 (talk) 00:58, 23 April 2021 (UTC)

Nonexistence
Having taught and researched game theory for almost 30 years, I have never before come across the term "intransitive game" (or "nontransitive game").

The definition given in the article makes no sense, since it is unclear what "strategy A is preferred over strategy B" means. The natural interpretation of "is preferred over" would be "dominates", but dominance is a transitive relation.

The reference to Rock-Paper-Scissors (RSP) implies that the intended interpretation of "is preferred over" is "is a best response to", which is a quite different concept. This interpretation is only applicable in symmetric games. However, transitivity of best responses in symmetric games is a nongeneric property, so almost every symmetric game would be "intransitive" under this interpretation and thus a specific term for this type of game wouldn't be justified.

A third possible interpretation would be that an "intransitive game" is a game with a best-response cycle (as RSP has). However, these games are simply called "games with a best-response cycle" in game theory. Moreover, it would be a mistake to equate the existence of best-response cycles with intransitivity, since these two properties don't contradict.

A fourth and final possibility would be to define an "intransitive game" as a symmetric zero-sum game with a best-response cycle (like RSP). In the class of zero-sum games, existence of best-response cycles indeed rules out transitivity of the best-response relation, but the combination of these two properties is very restrictive. E.g. any "intransitive game" with 3 strategies would be equivalent to RSP.

The only reference in the article is to a popular maths book by Martin Gardner. From the context it is likely that Gardner really had in mind the fourth interpretation. Nevertheless, the term "intransitive game" seems not to exist outside his book and a few online sources that reference his book.

It would be best to delete this article. 2001:628:404:47:7220:84FF:FE0C:F265 (talk) 10:32, 8 May 2023 (UTC)