title: Cyclic dominance in evolutionary games: a review.
abstract: 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.
authors.affiliation: Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, PO Box 49, 1525 Budapest, Hungary szolnoki.attila@ttk.mta.hu.
authors.forename: Attila
authors.identifier: http://orcid.org/0000-0002-0907-0406
authors.initials: A
authors.lastname: Szolnoki
authors.affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
authors.forename: Mauro
authors.initials: M
authors.lastname: Mobilia
authors.affiliation: College of Physics and Electronic Information Engineering, Wenzhou University, 325035 Wenzhou, People's Republic of China.
authors.forename: Luo-Luo
authors.initials: LL
authors.lastname: Jiang
authors.affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
authors.forename: Bartosz
authors.initials: B
authors.lastname: Szczesny
authors.affiliation: Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
authors.forename: Alastair M
authors.initials: AM
authors.lastname: Rucklidge
authors.affiliation: Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia matjaz.perc@uni-mb.si.
authors.forename: Matjaž
authors.identifier: http://orcid.org/0000-0002-3087-541X
authors.initials: M
authors.lastname: Perc
mesh_terms: D000328:Adult; D000818:Animals; D005717:Games, Experimental; D006801:Humans; D008962:Models, Theoretical
keywords: coevolution; cyclical interactions; mobility; pattern formation; phase transitions; self-organization