%0 Journal Article
%@ 2164-6066
%A Hofbauer, J.
%A Bednarik, P.
%D 2017
%F iiasa:14353
%I American Institute of Mathematical Sciences
%J Journal of Dynamics and Games
%K Best response dynamics, discretization, periodic orbits, rock-paper-scissors game
%N 1
%P 75-86
%R 10.3934/jdg.2017005
%T Discretized best-response dynamics for the rock-paper-scissors game
%U https://pure.iiasa.ac.at/id/eprint/14353/
%V 4
%X Discretizing a differential equation may change the qualitative behaviour drastically, even if the stepsize is small. We illustrate this by looking at the discretization of a piecewise continuous differential equation that models a population of agents playing the Rock-Paper-Scissors game. The globally asymptotically stable equilibrium of the differential equation turns, after discretization, into a repeller surrounded by an annulus shaped attracting region. In this region, more and more periodic orbits emerge as the discretization step approaches zero.