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We study a variant of the cyclic Lotka-Volterra model with three-agentinteractions. Inspired by a multiplayer variation of the Rock-Paper-Scissorsgame, the model describes an ideal ecosystem in which cyclic competition amongthree species develops through cooperative predation. Its rate equations in awell-mixed environment display a degenerate Hopf bifurcation, occurring asreactions involving two predators plus one prey have the same rate as reactionsinvolving two preys plus one predator. We estimate the magnitude of thestochastic noise at the bifurcation point, where finite size effects turnneutrally stable orbits into erratically diverging trajectories. In particular,we compare analytic predictions for the extinction probability, derived in theFokker-Planck approximation, with numerical simulations based on the Gillespiestochastic algorithm. We then extend the analysis of the phase portrait toheterogeneous rates. In a well-mixed environment, we observe a continuum ofdegenerate Hopf bifurcations, generalizing the above one. Neutral stabilityensues from a complex equilibrium between different reactions. Remarkably, on atwo-dimensional lattice, all bifurcations disappear as a consequence of thespatial locality of the interactions. In the second part of the paper, weinvestigate the effects of mobility in a lattice metapopulation model withpatches hosting several agents. We find that strategies propagate along thearms of rotating spirals, as they usually do in models of cyclic dominance. Weobserve propagation instabilities in the regime of large wavelengths. We alsoexamine three-agent interactions inducing nonlinear diffusion.

Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions