Journal of Dynamics and Games (JDG)

Discretized best-response dynamics for the rock-paper-scissors game

Pages: 75 - 86, Volume 4, Issue 1, January 2017      doi:10.3934/jdg.2017005

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Peter Bednarik - International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria (email)
Josef Hofbauer - Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, 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.
Mathematics Subject Classification:  Primary: 34A36, 91A22; Secondary: 34A60, 39A28.

Received: April 2016;      Revised: December 2016;      Available Online: December 2016.