Ordering structured populations in multiplayer cooperation games

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Social Dynamics

Background:

• Spatial structure significantly influences the evolution of cooperation in games.
• Comparing population structures in multiplayer games is complex due to multiple structure coefficients.

Purpose of the Study:

• To develop a standardized method for comparing population structures in evolutionary games.
• To establish criteria for determining which structures more effectively promote cooperation.

Main Methods:

• Introduction of the containment order and volume order for population structures.
• Derivation of conditions for establishing the containment order.
• General results for the volume order and application to spatial game models.

Main Results:

• The containment and volume orders provide a clear way to rank population structures based on their potential to promote cooperation.
• Conditions for the containment order are established, and general results for the volume order are presented.
• The theory is illustrated by comparing various spatial game models and update rules.

Conclusions:

• The proposed ordering methods simplify the analysis of cooperation evolution across diverse population structures.
• These findings offer a broadly applicable framework for understanding the role of spatial structure in social evolution.