# The Rock--Paper--Scissors Game

## TL;DR

This paper introduces Rock-Paper-Scissors as a model for decision-making and strategic interactions, explaining key concepts and reviewing recent theoretical and empirical studies on its non-equilibrium dynamics and applications.

## Contribution

It provides an accessible introduction to RPS for physics students and reviews recent advances in understanding its complex non-equilibrium behaviors and applications in ecology and economics.

## Key findings

- Collective cycling observed in RPS dynamics
- Conditional response patterns influence strategy stability
- Microscopic mechanisms promote cooperation in RPS models

## Abstract

Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no background in game theory, this paper introduces the concepts of Nash equilibrium and evolutionarily stable strategy, and reviews some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS, including collective cycling, conditional response patterns, and microscopic mechanisms that facilitate cooperation. We also introduce several dynamical processes to illustrate the applications of RPS as a simplified model of species competition in ecological systems and price cycling in economic markets.