Social learning with complex contagion.

Area of Science:

• Evolutionary Game Theory
• Social Learning Dynamics
• Complex Systems Modeling

Background:

• Traditional social learning models assume simple contagion, where one interaction suffices for imitation.
• Real-world behavior spread often involves complex contagion, necessitating multiple exposures for adoption.
• Existing models may not fully capture the nuances of behavioral change in social networks.

Purpose of the Study:

• To introduce a novel framework combining simple payoff-biased imitation with complex contagion.
• To model the spread of social behaviors in populations with realistic contagion dynamics.
• To analyze the impact of complex contagion on evolutionary game theory outcomes.

Main Methods:

• Formulated a discrete time and state stochastic process for social learning.
• Derived the continuum limit as an ordinary differential equation generalizing the replicator equation.
• Applied the model to linear frequency-dependent games, including the Prisoner's Dilemma, Snowdrift, and Coordination games.

Main Results:

• Complex contagion dynamics yield qualitatively different outcomes compared to traditional imitation.
• The Prisoner's Dilemma can shift from an all-defector equilibrium to a mixed or bistable system.
• The Snowdrift and Coordination games exhibit altered equilibrium structures under complex contagion.
• Outcomes depend on the interplay between contagion complexity and selection strength.

Conclusions:

• The framework provides a synthetic approach to understanding realistic behavioral change in social systems.
• Integrating complex contagion offers a more nuanced perspective on social learning and its evolutionary consequences.
• This work bridges evolutionary game theory and complex contagions for broader applicability.