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Multilayer networks influence coordination games. Higher node overlap synchronizes layers, favoring payoff-dominant equilibria with replicator dynamics (RD) and unconditional imitation (UI) update rules, unlike best response (BR).

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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.