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

Author(s)
Peter Bednarik, Josef Hofbauer
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.

Organisation(s)
Department of Economics, Department of Mathematics
Journal
Journal of Dynamics and Games
Volume
4
Pages
75-86
No. of pages
12
ISSN
2164-6066
DOI
https://doi.org/10.3934/jdg.2017005
Publication date
01-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
101017 Game theory
Keywords
ASJC Scopus subject areas
Applied Mathematics, Statistics and Probability, Modelling and Simulation
Portal url
https://ucris.univie.ac.at/portal/en/publications/discretized-bestresponse-dynamics-for-the-rockpaperscissors-game(83b74237-ca13-4bef-a8b1-6d5bc5f0504d).html