Discretized best-response dynamics for the rock-paper-scissors game
Peter Bednarik - International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria (email)
Abstract: 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.
Keywords: Best response dynamics, discretization, periodic orbits, rock-paper-scissors game.
Received: April 2016; Revised: December 2016; Available Online: December 2016.