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Global oscillations in the Optional Public Goods Game under spatial diffusion

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  • Valverde, Pablo A.
  • da Silva, Roberto
  • Stock, Eduardo V.

Abstract

Social dilemmas lead to natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the evolution of species. In order to comprehend the mechanisms involved in this framework, here we study the Optional Public Good Games with focus on the effects of diffusive aspects in the emergent patterns of cyclic dominance between the strategies. Differently from other works, we showed that rock–paper–scissors (RPS) patterns occur by introducing a simple kind of random mobility in a lattice sparsely occupied. Such pattern has been revealed to be very important in the conservation of the species in ecological and social environments. The goal of this paper is to show that we do not need more elaborated schemes for construction of the neighbourhood in the game to observe RPS patterns as suggested in the literature. As an interesting additional result, in this contribution we also propose an alternative method to quantify the RPS density in a quantitative context of the game theory which becomes possible to perform a finite size scaling study. Such approach can be very interesting to be applied in other games generically.

Suggested Citation

  • Valverde, Pablo A. & da Silva, Roberto & Stock, Eduardo V., 2017. "Global oscillations in the Optional Public Goods Game under spatial diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 61-69.
    • Handle: RePEc:eee:phsmap:v:474:y:2017:i:c:p:61-69
    DOI: 10.1016/j.physa.2017.01.056
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    References listed on IDEAS

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    1. Almeida, Enock & da Silva, Roberto & Martinez, Alexandre Souto, 2014. "Strategies generalization and payoff fluctuation optimization in the iterated ultimatum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 54-65.
    2. Zhong, Li-Xin & Xu, Wen-Juan & Shi, Yong-Dong & Qiu, Tian, 2013. "Coupled dynamics of mobility and pattern formation in optional public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 18-26.
    3. da Silva, Roberto & Bazzan, Ana L.C. & Baraviera, Alexandre T. & Dahmen, Sílvio R., 2006. "Emerging collective behavior and local properties of financial dynamics in a public investment game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 610-626.
    4. Christoph Hauert, 2006. "Cooperation, Collectives Formation And Specialization," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 315-335.
    5. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
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    Cited by:

    1. Pan, Jianchen & Zhang, Lan & Han, Wenchen & Huang, Changwei, 2023. "Heterogeneous investment promotes cooperation in spatial public goods game on hypergraphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    2. Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    3. Wang, Jianwei & Chen, Wei & Yu, Fengyuan & He, Jialu & Xu, Wenshu, 2022. "Wealth-based rule favors cooperation in costly public goods games when individual selection is inevitable," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    4. Xie, Kai & Liu, Xingwen & Chen, Hao & Yang, Jun, 2022. "Preferential selection and expected payoff drive cooperation in spatial voluntary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

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