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Random mobility and the evolution of cooperation in spatial N-player iterated Prisoner’s Dilemma games

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  • Chiong, Raymond
  • Kirley, Michael

Abstract

We study the effects of random mobility on the evolution of cooperation in a spatial version of the N-player Iterated Prisoner’s Dilemma game, where individuals are located on a two-dimensional regular lattice with periodic boundary conditions. The probability that an individual moves from its current location is based on the amount of time it has occupied a given position and the relative fitness values of the individual occupying the destination position. Our results show that random movement can promote cooperative behaviour in N-player games. In some circumstances, random mobility enhances system-wide cooperation levels when compared to the static model. However, the outcome is strictly dependent on the cost-to-benefit ratio and the range of movement. An analysis of the population dynamics suggests that the convergence rate of the model (i.e., the time for the population to reach an equilibrium state) is faster with mobility in place. Our findings help to further understand the relationship between mobility and evolving game-playing strategies in spatially structured populations, especially when efficient collective actions matter.

Suggested Citation

  • Chiong, Raymond & Kirley, Michael, 2012. "Random mobility and the evolution of cooperation in spatial N-player iterated Prisoner’s Dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3915-3923.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:15:p:3915-3923
    DOI: 10.1016/j.physa.2012.03.010
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    References listed on IDEAS

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    1. Zhang, Jianlei & Zhang, Chunyan & Chu, Tianguang, 2011. "The evolution of cooperation in spatial groups," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 131-136.
    2. Dirk Helbing & Wenjian Yu, 2008. "Migration As A Mechanism To Promote Cooperation," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 641-652.
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    4. Zhang, Jun & Wang, Wei-Ye & Du, Wen-Bo & Cao, Xian-Bin, 2011. "Evolution of cooperation among mobile agents with heterogenous view radii," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2251-2257.
    5. Chen, Zhuo & Gao, Jianxi & Cai, Yunze & Xu, Xiaoming, 2011. "Evolution of cooperation among mobile agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1615-1622.
    6. Chen, Zhuo & Gao, Jianxi & Cai, Yunze & Xu, Xiaoming, 2011. "Evolutionary prisoner’s dilemma game in flocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 50-56.
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    Cited by:

    1. Cheng, Jiangjiang & Mei, Wenjun & Su, Wei & Chen, Ge, 2023. "Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    2. Dhakal, Sandeep & Chiong, Raymond & Chica, Manuel & Middleton, Richard H., 2020. "Climate change induced migration and the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 377(C).

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