Cyclic dominance in evolutionary games: A review

Attila Szolnoki, Mauro Mobilia, Luo Luo Jiang, Bartosz Szczesny, Alastair M. Rucklidge, Matjaž Perc

Research output: Contribution to journalReview article

202 Citations (Scopus)


Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock- paper-scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined.

Original languageEnglish
Article number0735
JournalJournal of the Royal Society Interface
Issue number100
Publication statusPublished - Nov 6 2014


  • Coevolution
  • Cyclical interactions
  • Mobility
  • Pattern formation
  • Phase transitions
  • Self-organization

ASJC Scopus subject areas

  • Biotechnology
  • Biophysics
  • Bioengineering
  • Biomaterials
  • Biochemistry
  • Biomedical Engineering

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    Szolnoki, A., Mobilia, M., Jiang, L. L., Szczesny, B., Rucklidge, A. M., & Perc, M. (2014). Cyclic dominance in evolutionary games: A review. Journal of the Royal Society Interface, 11(100), [0735].