Cyclic dominance in evolutionary games: a review

  title={Cyclic dominance in evolutionary games: a review},
  author={Attila Szolnoki and Mauro Mobilia and Luo-Luo Jiang and Bartosz Szczesny and Alastair M. Rucklidge and Matja{\vz} Perc},
  journal={Journal of The Royal Society Interface},
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… 

The rock–paper–scissors game

The concepts of Nash equilibrium and evolutionarily stable strategy are introduced and some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS are reviewed, including collective cycling, conditional response patterns and microscopic mechanisms that facilitate cooperation.

Rock-paper-scissors played within competing domains in predator-prey games

The linear stability analysis predicts the number of forming domains, their composition in terms of species; it also explains the instability of interfaces between domains, which drives their extinction; spiral patterns are identified as motion along heteroclinic cycles.

Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers

The results demonstrate that protection spillovers may fundamentally change the dynamics of cyclic dominance in structured populations, and they outline the possibility of programming pattern formation in microbial populations.

Mistakes can stabilise the dynamics of rock-paper-scissors games

This work considers an unstable version of rock-paper-scissors dynamics and allows individuals to make behavioural mistakes during the strategy execution, showing analytically that heterogeneity in behavioural patterns may break a cyclic relationship and lead to a stable equilibrium in pure or mixed strategies.

Spatial organization, grouping strategies and cyclic dominance in asymmetric predator-prey games

The Lett-Auger-Gaillard model is extended to spatially distributed groups and it is shown that the coexistence phase in which both strategies for each group are present is stable because of an effective, cyclic dominance behavior similar to the Rock-Paper-Scissors game with four species.

Emergence of unusual coexistence states in cyclic game systems

This work investigates the effect of nonuniform intraspecific competitions on coexistence and finds that a wider spectrum of coexistence states can emerge and persist and indicates that intraspecities can promote biodiversity to a broader extent than previously thought.

Ecology shapes the cyclic dominance games between Escherichia coli strains

This work showed the advantage and vast potential of integrating ecology into evolutionary game models for understanding and predicting evolutionary dynamics in biologically realistic contexts.

Aggregation as an antipredator strategy in the rock-paper-scissors model




Effects of competition on pattern formation in the rock-paper-scissors game.

It is found that competition is vital for the sustenance of biodiversity and the emergence of pattern formation in ecosystems governed by cyclical interactions, and increases with increasing system size because noise reinforces the disintegration of ordered patterns.

Population interaction structure and the coexistence of bacterial strains playing ‘rock–paper–scissors’

This work extends the Kerr et al. model to include different (aspatial) population network structures with the same degree distributions as corresponding spatial lattice models, and shows that the coexistence that occurs for some parameter combinations when simulated bacterial strains compete on lattices is absent when they compete on random regular graphs.

Cyclic dominance in adaptive networks

This work shows analytically and numerically that nonequilibrium phase transitions occur as a function of the rewiring strength, and presents a detailed analysis of the corresponding transitions revealing an apparently paradoxical behavior.

From pairwise to group interactions in games of cyclic dominance.

It is shown that differences in the interaction range affect not only the stationary fractions of strategies but also their relations of dominance, and the transition from pairwise to group interactions can decelerate and even revert the direction of the invasion between the competing strategies.

Rock–scissors–paper and the survival of the weakest

  • Marcus FreanE. Abraham
  • Economics
    Proceedings of the Royal Society of London. Series B: Biological Sciences
  • 2001
This work considers a system with three species in a competitive loop and shows that this simple ecology exhibits two counter–intuitive phenomena, analogous to the tragedy of the commons, but here, rather than leading to a collapse, the ‘tragedy’ acts to maintain diversity.

Globally synchronized oscillations in complex cyclic games.

It is shown that upon replacing a minimum fraction Q of the short-range interactions by long-range ones, there is a Hopf bifurcation, and global oscillations become stable, even for large, realistic food webs.

Four-state rock-paper-scissors games in constrained Newman-Watts networks.

It is concluded that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.

Clonal selection prevents tragedy of the commons when neighbors compete in a rock-paper-scissors game.

This work explores the evolution of a rock-paper-scissors system where three species compete for space and shows that when only one species mutates, group selection removes individual predators with the fastest growth rates, causing the growth rate of the species to stabilize.

Characterization of spiraling patterns in spatial rock-paper-scissors games.

A generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals is considered, and the properties of the spiraling patterns arising in each phase are characterized.

Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games

It is established that this phenomenon is robust; it does not depend on the details of cyclic competition or spatial environment, and are relevant for the formation and propagation of patterns in microbial populations or excitable media.