Seminár z kvalitatívnej teórie diferenciálnych rovníc - Peter Bednarik (25.2.2016)
vo štvrtok 25.2.2016 o 14:00 hod. v miestnosti M/223
Prednášajúci: Peter Bednarik (IIASA Laxenburg)
Názov prednášky: Discretized best-response dynamics for cyclic games
Termín: 25.2.2016, 14:00 hod., M/223
Abstract:
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.