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On evolution of agent behavior under limited gaming time with reinforcement learning

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  • Li, Dandan
  • Wu, Qiongzi
  • Han, Dun

Abstract

Based on the prisoner’s dilemma (PD) evolutionary game model and reinforcement learning framework, this paper studies the impact of factors such as temptation payoff, time allocation, and others on agent behavior evolution and strategy selection under limited gaming time resources, across three different agent relationship structures. The results show that an increase in the agent’s gaming time resources and lower temptation payoffs, or the agent’s greater emphasis on long-term rewards and avoidance of excessive behavioral adjustments, all contribute to promoting cooperation between agents. Additionally, the total remaining gaming time between agents gradually increases as the game progresses, while the total gaming time between agents gradually decreases. Both will eventually reach a steady state after a sufficiently large number of game rounds. Further results indicate that an increase in temptation payoff leads to an increase in total remaining gaming time, while reducing the total gaming time between agents. Finally, the measure of heterogeneity in gaming time distribution between agents gradually increases throughout the game process. This is particularly evident when the temptation payoff is high, as the differences in gaming time allocation between agents increase, significantly enhancing the heterogeneity of gaming time among agents in the system. This study provides important theoretical support for understanding agent behavior evolution under limited gaming time resources, especially in dynamic cooperative and competitive game scenarios.

Suggested Citation

  • Li, Dandan & Wu, Qiongzi & Han, Dun, 2025. "On evolution of agent behavior under limited gaming time with reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001791
    DOI: 10.1016/j.chaos.2025.116166
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    References listed on IDEAS

    as
    1. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Jie, Yingmo & Liu, Charles Zhechao & Choo, Kim-Kwang Raymond & Guo, Cheng, 2024. "An incentive compatible ZD strategy-based data sharing model for federated learning: A perspective of iterated prisoner's dilemma," European Journal of Operational Research, Elsevier, vol. 315(2), pages 764-776.
    3. Han, Dun & Wang, Xiao, 2023. "Vaccination strategies and virulent mutation spread: A game theory study," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Chaoqian Wang & Matjaž Perc & Attila Szolnoki, 2024. "Evolutionary dynamics of any multiplayer game on regular graphs," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    5. Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2025. "The effect of ecological compensation on a coevolutionary common pool resource game," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    6. Han, Dun & He, Youxin, 2023. "The impact of labor subsidy, taxation and corruption on individual behavior," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    7. Yue, Hongyu & Xiong, Xiaojin & Feng, Minyu & Szolnoki, Attila, 2025. "Coevolution of relationship-driven cooperation under recommendation protocol on multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    8. İzgi, Burhaneddin & Özkaya, Murat & Kemal Üre, Nazım & Perc, Matjaž, 2025. "A holistic matrix norm-based alternative solution method for Markov reward games," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    9. Li, Dandan & Zhou, Kai & Sun, Mei & Han, Dun, 2023. "Investigating the effectiveness of individuals’ historical memory for the evolution of the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    10. Ma, Yuanyuan & Zhang, Qiannan & Xie, Leilei, 2025. "A study on multi-information diffusion model considering dual social reinforcement effect from the perspective of evolutionary game," Applied Mathematics and Computation, Elsevier, vol. 492(C).
    11. Li, Xiaopeng & Wang, Zhonglin & Xu, Yan & Zhang, Hui & Yu, Guihai, 2024. "Asymmetrical interactions driven by strategic persistence effectively alleviate social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    12. Ling, Ting & Li, Zhang & Feng, Minyu & Szolnoki, Attila, 2025. "Supervised cooperation on interdependent public goods games," Applied Mathematics and Computation, Elsevier, vol. 492(C).
    13. Valerio Capraro & Roberto Di Paolo & Matjaz Perc & Veronica Pizziol, 2024. "Language-based game theory in the age of artificial intelligence," Papers 2403.08944, arXiv.org.
    14. Xu, Wei & Li, Dandan & Han, Dun & Sun, Mei, 2024. "The impact of relationship stickiness and memory on the evolution of individual behavior," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    15. Xiao, Lu & Liu, Jianyue & Ge, Jinwen, 2021. "Dynamic game in agriculture and industry cross-sectoral water pollution governance in developing countries," Agricultural Water Management, Elsevier, vol. 243(C).
    16. Ding, Rui & Wang, Xianjia & Zhao, Jinhua & Gu, Cuiling, 2025. "Effects of punishment driven by inequity aversion on promoting cooperation in public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    17. Shen, Yong & Ma, Yujie & Kang, Hongwei & Sun, Xingping & Chen, Qingyi, 2024. "Learning and propagation: Evolutionary dynamics in spatial public goods games through combined Q-learning and Fermi rule," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
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