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Seminar 25.2.2016: Peter Bednarik

PostPosted: Fri Feb 19, 2016 11:03 am
by quittner
Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Štvrtok 25.2.2016 o 14:00, poslucháreň M-223

Peter Bednarik (IIASA Laxenburg):
Discretized best-response dynamics for cyclic games

Many evolutionary models use continuous-time dynamics to simplify from discrete-time events.
This does not always need to be structurally stable. As an example, we examined the behavior
of the best-response dynamics for cyclic games such as the Rock-Paper-Scissors game.
The differences to the continuous-time version are remarkable. In particular, by discretization,
asymptotically stable fixed points can turn into repellers surrounded by an annulus shaped
attracting region. In this region, more and more periodic orbits emerge as the discretization step
gets smaller. We provided a geometric proof and measured the inner and outer radius
of the attracting region that is replacing an attracting point and investigated what happened
when scaling down the discretization step, i.e. moving towards the continuous-time version.
In addition, we ran numerical simulations to demonstrate the results visually.