The rock–paper–scissors game

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.

Keywords:

• cyclic dominance
• non-cooperative game
• decision making
• social cycling
• conditional response
• non-equilibrium

Acknowledgements

I thank Prof Bin Xu and Dr Zhijian Wang for collaborations, and thank Prof Bin Xu for a critical reading of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is partially supported by the National Basic Research Program of China [grant number 2013CB932804] and by the National Natural Science Foundations of China [grant number 11121403] and [grant number 11225526].