A solution for private assessment in indirect reciprocity using solitary observation

Area of Science:

• Evolutionary game theory
• Social dynamics
• Behavioral economics

Background:

• Indirect reciprocity is a key driver of cooperation evolution.
• Most research assumes public assessment, limiting understanding of private information's role.
• Analytical challenges have historically confined private assessment studies to simulations.

Purpose of the Study:

• To develop an analytical method for studying indirect reciprocity under private assessment.
• To investigate the impact of private assessment on the evolution of cooperation norms.
• To compare the stability and cooperation rates of different indirect reciprocity norms in private assessment scenarios.

Main Methods:

• Formulation of a solitary observation model for private assessment.
• Calculation of replicator dynamics for five leading indirect reciprocity norms.
• Analytical investigation of cooperative evolutionarily stable (CES) points without approximation.

Main Results:

• Private assessment yields different outcomes than public assessment for indirect reciprocity norms.
• Strict norms (stern judging, shunning) lack CES points in private assessment, unlike public.
• Tolerant norms (simple standing, staying) lead to co-existence of norms and unconditional cooperators, increasing overall cooperation rates.

Conclusions:

• Private assessment can enhance cooperation by enabling unconditional cooperators to play a role.
• The 'staying' norm demonstrates superiority over 'simple standing' in private assessment due to higher cooperation, easier invasion of defectors, and robustness.
• Careful selection of norms and assessment rules is crucial for fostering cooperation in social dilemmas involving private information.