title: Synchronization and extinction in cyclic games with mixed strategies.
abstract: We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing β balls of three and four types, respectively, where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy. Using both mean-field rate equations and numerical simulations, we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time-dependent probability distributions. For the three-strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution. For large values of β, yielding a good approximation to a continuous distribution, spatially synchronized temporal oscillations dominate the system. For the four-strategy game the system is always neutrally stable, but different regimes emerge, depending on the size of the system and the level of discretization.
authors.affiliation: Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.
authors.forename: Ben
authors.initials: B
authors.lastname: Intoy
authors.affiliation: Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.
authors.forename: Michel
authors.initials: M
authors.lastname: Pleimling
mesh_terms: D005716:Game Theory; D008962:Models, Theoretical; D011336:Probability; D013997:Time Factors