Exact cluster dynamics of indirect reciprocity in complete graphs

Area of Science:

• Social Psychology
• Game Theory
• Computational Social Science

Background:

• Heider's balance theory posits cognitive consistency in social assessments.
• Indirect reciprocity theory models cooperation through reputation and assessment dynamics.
• The "leading eight" norms guide social interactions in dilemmas.

Purpose of the Study:

• To investigate the relationship between cognitive balance and dynamic assessment norms.
• To analyze the population-level consequences of specific social norms, particularly stern judging (L6) and L4.
• To understand how individual assessment rules lead to emergent societal structures.

Main Methods:

• Mathematical analysis of dynamical systems on complete graphs.
• Comparison of norm dynamics, specifically stern judging (L6) and L4.
• Simulation of agent-based interactions under different normative rules.

Main Results:

• Balance theory aligns with dynamic stationarity only for norms L4 and L6.
• Stern judging (L6) dynamics lead to population segregation into hostile groups.
• Norm L4, unlike L6, fosters a cooperative "paradise" with abundant positive assessments.

Conclusions:

• Individual norms have profound emergent consequences on population dynamics.
• Subtle differences in assessment rules (L4 vs. L6) drastically alter societal outcomes.
• Cognitive consistency and segregation dynamics are intricately linked through social norms.