Partner selections in public goods games with constant group size

Area of Science:

• Evolutionary Game Theory
• Social Dynamics
• Behavioral Economics

Background:

• Previous public goods game models often assume unconditional participation or variable group sizes.
• The impact of fixed group sizes, common in social institutions, on cooperation evolution remains understudied.

Purpose of the Study:

• To investigate how fixed group sizes influence the evolution of cooperation in public goods games.
• To compare degree-based and reputation-based partner selection mechanisms in promoting cooperation.

Main Methods:

• A mathematical model was developed where individuals select a fixed number of interaction partners.
• Partner selection probabilities were based on neighbor degrees or reputations, creating dynamical group formation.
• The study analyzed stationary densities of cooperators under different selection regimes and group sizes.

Main Results:

• Monotonic dependence of cooperator density on group size was observed in both degree-based and reputation-based selection.
• Reputation-based partner selection demonstrated a substantial improvement in cooperation levels.
• Extended models included preferences for social ties and random selection on regular graphs for comparison.

Conclusions:

• Fixed group sizes can be effectively modeled to study cooperation evolution.
• Reputation plays a crucial role in fostering cooperation within structured social networks.
• The findings offer insights into real-world teamwork and cooperation dynamics.