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

Hofbauer, J. & Bednarik, P. (2017). Discretized best-response dynamics for the rock-paper-scissors game. Journal of Dynamics and Games 4 (1) 75-86. 10.3934/jdg.2017005.

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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.

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