Evolutionary games on multilayer networks: coordination and equilibrium selection

TL;DR

This paper investigates how multilayer networks influence synchronization and equilibrium selection in two-player coordination games using evolutionary game theory, revealing critical thresholds and symmetry-breaking effects across different update rules.

Contribution

It introduces a novel multilayer network framework to study coordination and equilibrium selection, highlighting the impact of inter-layer connectivity and update rules.

Findings

Synchronization depends on inter-layer overlap $q$ and payoff difference $\

Multilayer structure enhances Pareto-optimal equilibrium prevalence.

Symmetry breaking leads to exclusive selection of payoff-dominant strategies.

Abstract

We study mechanisms of synchronisation, coordination, and equilibrium selection in two-player coordination games on multilayer networks. We apply the approach from evolutionary game theory with three possible update rules: the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). Players interact on a two-layer random regular network. The population on each layer plays a different game, with layer I preferring the opposite strategy to layer II. We measure the difference between the two games played on the layers by a difference in payoffs $\Delta S$ while the inter-connectedness is measured by a node overlap parameter $q$. We discover a critical value $q_c(\Delta S)$ below which layers do not synchronise. For $q>q_c$ in general both layers coordinate on the same strategy. Surprisingly, there is a symmetry breaking in the selection of equilibrium -- for RD and UI there is a phase where only the payoff-dominant equilibrium is selected. Our work is an example of previously observed differences between the update rules on a single network. However, we took a novel approach with the game being played on two inter-connected layers. As we show, the multilayer structure enhances the abundance of the Pareto-optimal equilibrium in coordination games with imitative update rules.