Chaotic Dynamics in Asymmetric Rock-Paper-Scissors Games

Abstract

Evolutionary game dynamics is a combination of game theory and dynamical systems. Using dynamical theory, we investigate chaotic behavior in asymmetric Rock-Paper-Scissors games under imitative dynamics with two different populations. Our theoretical analysis and numerical simulations demonstrate that the dynamical system can give rise to chaotic behavior in zero-sum and positive-sum asymmetric games. However, chaos cannot occur in a negative-sum asymmetric game. In particular, the numerical simulations show that there is a limit cycle in a negative-sum asymmetric game.

Keywords

• Evolutionary game
• imitative dynamics
• chaos
• rock-paper-scissors