We study a class of algebras we regard as generalized rock–paper–scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study their automorphisms, and determine their congruence lattices. We produce a family of finite simple algebras.

中文翻译：

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多人石头剪刀布

我们研究了一类代数，我们将其视为广义的剪刀石头布博弈。我们确定何时可以存在此类代数，证明这些代数生成由超竞赛代数生成的变体，对这些代数进行计数，研究其自同构并确定它们的全等格。我们产生了一个有限简单代数族。