New doubly-anomalous Parrondo’s games suggest emergent sustainability and inequality

  • Jin Ming Koh
  • Kang Hao CheongEmail author
Original Paper


Parrondo’s games to date have largely focused on the dynamics of capital mean, and not capital spread—the potential of the framework in modelling ecological and socioeconomic sustainability and inequality has thus been ignored. Based on behavioural heuristics of distinct individualistic and multipartite interactive strategies, we introduce a novel multi-agent Parrondo game structure with dynamics dependent upon local inequality. Intriguingly, we observe the presence of doubly-anomalous scenarios, in which there is paradoxical population growth despite both pure strategies being losing, simultaneously accompanied by a suppression of inter-population capital variance to within constant bounds. Ecologically, this reflects sustainable population proliferation amidst disadvantageous conditions; the converse scenario in turn corresponds to inequality-plagued unsustainable growth. Different connectivity topologies, such as scale-free and random networks, are also investigated.


Parrondo’s paradox Population dynamics Ecology Game theory Complexity Cooperative Parrondo 



Kang Hao Cheong acknowledges the support of SUTD Start-up Research Grant (SRG).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11071_2019_4788_MOESM1_ESM.pdf (127 kb)
Supplementary material 1 (pdf 127 KB)


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Science and Math ClusterSingapore University of Technology and DesignSingaporeSingapore
  2. 2.Engineering ClusterSingapore Institute of TechnologySingaporeSingapore

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