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Replicator dynamics of division of labor games with delayed payoffs in infinite populations

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  • Yuan, Hairui
  • Meng, Xinzhu

Abstract

In recent years, the division of labor game has received widespread attention, however, the time delay in payoffs has been ignored. Hence, in this paper, we consider that there is a time delay for the player to gain the payoffs in the game, and the delay in payoffs leads to a Hopf bifurcation. When the time delay is greater than the critical time delay, the replicator dynamics oscillates near the equilibrium point, the critical time delay is determined by the cost difference between the two tasks and the cooperation benefits between the two players. We obtain the expression of the critical time delay by applying the characteristic equation analysis method, and clearly analyze various cases through observation and numerical simulation. With the increase of time delays, the dynamic system shows a transition from asymptotic stability to oscillation near equilibrium.

Suggested Citation

  • Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of division of labor games with delayed payoffs in infinite populations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002685
    DOI: 10.1016/j.chaos.2022.112058
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    References listed on IDEAS

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    1. Qin, Shipeng & Zhang, Gang & Tian, Haiyan & Hu, Wenjun & Zhang, Xiaoming, 2020. "Dynamics of asymmetric division of labor game with environmental feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).
    2. Chongyi Zhong & Hui Yang & Zixin Liu & Juanyong Wu, 2020. "Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
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    Cited by:

    1. Zhao, Zhengwu & Zhang, Chunyan, 2023. "The mechanisms of labor division from the perspective of task urgency and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of the Hawk-Dove game with different stochastic noises in infinite populations," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Sun, Qingqing & Chen, Hong & Long, Ruyin & Yang, Jiahui, 2023. "Who will pay for the “bicycle cemetery”? Evolutionary game analysis of recycling abandoned shared bicycles under dynamic reward and punishment," European Journal of Operational Research, Elsevier, vol. 305(2), pages 917-929.
    4. Wettergren, Thomas A., 2023. "Replicator dynamics of evolutionary games with different delays on costs and benefits," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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