Analysis of Multilevel Replicator Dynamics for General Two-Strategy Social Dilemma

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Social Dynamics

Background:

• Multilevel selection models examine competition at individual and group levels.
• Social dilemmas involve conflicts between individual and group interests, such as cooperation vs. defection.

Purpose of the Study:

• To analyze the dynamics of multilevel social dilemmas using a two-level replicator dynamics model.
• To extend analysis to all two-player, two-strategy social dilemmas, overcoming limitations of previous studies.

Main Methods:

• Utilized a nonlocal hyperbolic partial differential equation (PDE) for deterministic birth-death dynamics.
• Employed comparison principles and population distribution tail properties for broader applicability.
• Investigated specific game types: Stag-Hunt, Prisoner's Dilemma, and Hawk-Dove game.

Main Results:

• Any level of between-group competition can lead to cooperation fixation in Stag-Hunt games.
• Characterized selection thresholds in Prisoner's Dilemma and Hawk-Dove games, distinguishing between convergence to within-group equilibria and enhanced cooperation.
• Identified a trade-off between individual defection incentives and group-level cooperation benefits influencing steady-state payoffs.

Conclusions:

• Between-group competition is crucial for fostering cooperation in multilevel social dilemmas.
• Individual-level selection pressures can persistently limit cooperation, irrespective of group selection strength.
• The dynamics reveal complex interactions between individual and group selection in shaping population behavior.