Self-organizing patterns in an evolutionary rock-paper-scissors game for stochastic synchronized strategy updates

Area of Science:

• Evolutionary Game Theory
• Complex Systems
• Spatial Dynamics

Background:

• Rock-paper-scissors games model strategic interactions.
• Synchronized strategy updates are crucial in evolutionary dynamics.
• Noise and spatial structure influence game outcomes.

Purpose of the Study:

• To investigate the impact of synchronized strategy updating in a spatial rock-paper-scissors game.
• To analyze the emergence of oscillations and spatial patterns under varying noise levels.
• To understand invasion and speciation dynamics at domain interfaces.

Main Methods:

• Simulations of a spatial evolutionary rock-paper-scissors game on a square lattice.
• Implementation of synchronized strategy updates using the logit rule (noisy best-response).
• Analysis of system behavior in the zero noise limit and at low noise values.

Main Results:

• Two global oscillations with periods of three and six generations observed in the zero noise limit.
• Emergence of all nine oscillating phases at low noise values.
• Formation of self-organizing spatial patterns driven by invasion and speciation at interfaces.

Conclusions:

• Synchronized updates in spatial games can generate complex oscillatory behaviors.
• Noise plays a critical role in pattern formation and the diversity of dynamics.
• The model captures fundamental aspects of invasion, speciation, and spatial self-organization.