2,199 research outputs found
Riemannian game dynamics
We study a class of evolutionary game dynamics defined by balancing a gain
determined by the game's payoffs against a cost of motion that captures the
difficulty with which the population moves between states. Costs of motion are
represented by a Riemannian metric, i.e., a state-dependent inner product on
the set of population states. The replicator dynamics and the (Euclidean)
projection dynamics are the archetypal examples of the class we study. Like
these representative dynamics, all Riemannian game dynamics satisfy certain
basic desiderata, including positive correlation and global convergence in
potential games. Moreover, when the underlying Riemannian metric satisfies a
Hessian integrability condition, the resulting dynamics preserve many further
properties of the replicator and projection dynamics. We examine the close
connections between Hessian game dynamics and reinforcement learning in normal
form games, extending and elucidating a well-known link between the replicator
dynamics and exponential reinforcement learning.Comment: 47 pages, 12 figures; added figures and further simplified the
derivation of the dynamic
Selected topics on reaction-diffusion-advection models from spatial ecology
We discuss the effects of movement and spatial heterogeneity on population
dynamics via reaction-diffusion-advection models, focusing on the persistence,
competition, and evolution of organisms in spatially heterogeneous
environments. Topics include Lokta-Volterra competition models, river models,
evolution of biased movement, phytoplankton growth, and spatial spread of
epidemic disease. Open problems and conjectures are presented
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