Fence-sitters protect cooperation in complex networks.

Area of Science:

• Evolutionary game theory
• Complex networks
• Agent-based modeling

Background:

• Evolutionary game theory is vital across scientific disciplines.
• Previous studies in complex networks often rely on numerical simulations due to challenges with replicator dynamics.
• Analytical approaches are needed for deeper insights into strategy evolution.

Purpose of the Study:

• To introduce a vectorial formulation for analytically deriving individual payoffs in evolutionary games.
• To investigate the role of 'fence-sitters' in strategy evolution within complex networks.
• To explore how 'payoff memory' influences cooperation levels.

Main Methods:

• Developed a vectorial formalization applicable to two-strategy games.
• Defined 'fence-sitters' as individuals altering strategies during evolution.
• Introduced 'payoff memory' as a parameter to quantify aggregated payoffs over rounds.

Main Results:

• Successfully derived payoffs for pure cooperators, pure defectors, and fence-sitters analytically.
• Demonstrated that payoff memory effectively controls fence-sitter influence and cooperation levels.
• Observed that fence-sitters indirectly protect cooperation in complex network topologies.

Conclusions:

• The vectorial approach offers a general method for analyzing two-strategy evolutionary games.
• Fence-sitters have a significant, indirect role in promoting cooperation, especially when defection is tempting.
• This work enhances understanding of cooperative dynamics in complex systems.