Evolutionary games on multilayer networks: coordination and equilibrium selection

Abstract

We study mechanisms of synchronisation, coordination, and equilibrium selectionin two-player coordination games on multilayer networks. We apply the approach from evolutionary game theory with threepossible 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 layersby a difference in payoffs ∆ S while the inter-connectedness is measured by a node overlap parameter q. We discover a critical value qc(∆ S) below whichlayers do not synchronise. For q>qc in general both layerscoordinate on the same strategy. Surprisingly, there is a symmetry breakingin the selection of equilibrium -- for RD and UI there isa 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 playedon 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.