Assuming there are at least 3 alleles of the gene $G$ in total - $G_R$, $G_S$ and $G_P$ - is there any gene for which the following is true?
$G_R$ is more dominant than $G_S$.
$G_S$ is more dominant than $G_P$.
$G_P$ is more dominant than $G_R$.
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2$\begingroup$ Note that the "rock-paper-scissors pattern" is more formally known as a "non-transitive relation". You may be familiar with a transitive relation, where if A>B and B>C, then A>C. If instead A>B and B>C, but A<C (C>A), then it's known as a non-transitive relation, like the one you describe here. $\endgroup$– electronpusherCommented Nov 4, 2019 at 9:48
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A quick search gives this same question in this Reddit post.
Apparently, there is not yet an existing example of such dominance of three alleles on one another.
That said, if you're interested in rock-paper-scissor patterns in nature, then you will be interested in the side-blotched lizard. It has three genetically encoded male "sexes", that also determines their behaviour. At a population level, the three sexes follow a rock-paper-scissor pattern of successful sexual competition, in that orange-throated individuals can outcompete yellow-throated ones, which can outcompete blue-throated ones, which can outcome orange-throated ones. A simulation has been carried out to model the underlying genetics, but that model doesn't involve a rock-paper-scissors pattern of genetic dominance.
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$\begingroup$ @ruakh You mean "outcompete", not "outcome". $\endgroup$ Commented Nov 3, 2019 at 3:12
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$\begingroup$ @CJDennis: Yeah, I noticed that typo a few days after proposing the edit. (I also should have written something like "[...] but to be clear, that model [...]" instead of just "but that model".) But given that the edit took almost two weeks to get approved, it doesn't seem worth proposing a new edit just to fix such minor issues. :-/ $\endgroup$– ruakhCommented Nov 3, 2019 at 3:58
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$\begingroup$ @ruakh Too late now, but you can edit your edit before its approved. $\endgroup$ Commented Nov 3, 2019 at 4:15
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$\begingroup$ @CJDennis: Oh! Oops. Good to know. :-P $\endgroup$– ruakhCommented Nov 3, 2019 at 4:24