Introducing a graph topology for robust cooperation

Area of Science:

• Evolutionary Game Theory
• Network Science
• Computational Social Science

Background:

• Cooperation's emergence in spatial evolutionary game theory is extensively studied.
• The Prisoner's Dilemma on graphs models interactions with local constraints.

Purpose of the Study:

• To identify conditions ensuring cooperative populations resist initial defectors in spatial evolutionary games.
• To introduce and analyze a novel graph structure with inherent robustness against perturbations.

Main Methods:

• Utilized the Prisoner's Dilemma as the interaction model on graph-structured populations.
• Employed a neighborhood-based strategy update mechanism (copying the best strategy).
• Developed and proved properties of a specific graph structure ensuring initial cooperative robustness.

Main Results:

• Introduced a graph structure where a fully cooperative population is robust to single-agent defection.
• Provided a mathematical proof for this robustness property and specified graph constraints.
• Determined the smallest graph exhibiting this property and proposed methods for scaling it.

Conclusions:

• The identified graph structure offers a foundational model for robust cooperation in spatial evolutionary games.
• Empirical results demonstrate the extended graph's resilience to increasing percentages of defectors.
• A new class of graphs is proposed for future research into cooperation dynamics.