# Multiplayer Rock-Paper-Scissors

## TL;DR

This paper explores a class of generalized Rock-Paper-Scissors algebras, analyzing their existence, structure, automorphisms, and congruence lattices, and introduces finite simple algebras within this framework.

## Contribution

It characterizes when these algebras can exist and provides a detailed structural analysis, including automorphisms and congruence lattices, of a new class of generalized RPS algebras.

## Key findings

- Determined conditions for the existence of these algebras
- Generated varieties from hypertournament algebras
- Produced a family of finite simple algebras

## 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.