Evolutionary games on multilayer networks: coordination and equilibrium selection

Raducha, Tomasz; San Miguel Maxi
Submitted (2023)

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 ∆S while the inter-connectedness is measured
by a node overlap parameter q. We discover a critical value qc(∆S) below which layers do not synchronise. For q > qc 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.

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