Reciprocity in spatial evolutionary public goods game on double-layered network.

Jinho Kim,Yup Kim,Soon-Hyung Yook

doi:10.1038/srep31299

Jinho Kim, Yup Kim + Show 1 more

Open Access

https://doi.org/10.1038/srep31299

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Abstract

Spatial evolutionary games have mainly been studied on a single, isolated network. However, in real world systems, many interaction topologies are not isolated but many different types of networks are inter-connected to each other. In this study, we investigate the spatial evolutionary public goods game (SEPGG) on double-layered random networks (DRN). Based on the mean-field type arguments and numerical simulations, we find that SEPGG on DRN shows very rich interesting phenomena, especially, depending on the size of each layer, intra-connectivity, and inter-connected couplings, the network reciprocity of SEPGG on DRN can be drastically enhanced through the inter-connected coupling. Furthermore, SEPGG on DRN can provide a more general framework which includes the evolutionary dynamics on multiplex networks and inter-connected networks at the same time.

Highlights

To understand how the coupling between networks develops the cooperation or the network reciprocity, in this report, we investigate the spatial evolutionary public goods game (SEPGG) on double-layered random networks (DRN’s)
Depending on the multiplication factor r and the size of graph N, either Loner-only state (L-state), which is the anomalous state with no active participants, or Defector-only state (D-state), which means the state of “tragedy of the commons”, has been shown to appear on CG17
When p = 0, there exists no coupling between the layers and the steady-states of each layers are the same as those on a single random network, which we have already studied in ref

Summary

Previous Study

To understand “Tragedy of the commons”[48] problem with large participants has been studied through the SEPGG on the complete graph (CG) and dense random networks[17]. Depending on the multiplication factor r and the size of graph N, either Loner-only state (L-state), which is the anomalous state with no active participants, or Defector-only state (D-state), which means the state of “tragedy of the commons”, has been shown to appear on CG17. We have shown the following crossover behaviors as the mean-degree 〈k〉of underlying random networks changes[17]. We have been found that cooperation gradually increases as the number of participants or 〈k〉decreases, which is the origin of these crossovers. The crossovers describe how the enhanced cooperation on sparse networks overcomes “tragedy of the commons” on dense networks

Results

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Discussion

Additional Information