Multiplayer Rock-Paper-Scissors

Abstract

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.

Submitted to the special Topical Collection of Algebra Universalis honoring Ralph Freese, Bill Lampe, and JB Nation