Evolutionary games on multilayer networks: coordination and equilibrium selection

Area of Science:

• Game Theory
• Network Science
• Computational Social Science

Background:

• Coordination games are fundamental to understanding strategic interactions.
• Multilayer networks offer a more realistic framework for complex social and biological systems.
• Understanding equilibrium selection is crucial in game theory.

Purpose of the Study:

• To investigate synchronization, coordination, and equilibrium selection in two-player coordination games on multilayer networks.
• To analyze the impact of network structure and update rules on game outcomes.
• To explore how multilayer interactions affect the emergence of specific equilibria.

Main Methods:

• Simulations of two-player coordination games on a two-layer random regular network.
• Implementation and comparison of three update rules: replicator dynamics (RD), best response (BR), and unconditional imitation (UI).
• Analysis of varying node overlap (inter-connectedness) and payoff differences between layers.

Main Results:

• A critical node overlap threshold was identified, below which layers fail to synchronize and display different coordination levels.
• Above the threshold, both layers tend to coordinate on the same strategy.
• Symmetry breaking in equilibrium selection was observed for RD and UI, favoring the payoff-dominant equilibrium, but not for BR.

Conclusions:

• Multilayer network structure significantly impacts coordination game dynamics and equilibrium selection.
• The degree of inter-connectedness (node overlap) is critical for layer synchronization.
• Imitative update rules, combined with multilayer structures, can enhance the prevalence of the Pareto-optimal equilibrium in coordination games.