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An escort replicator dynamic with a continuous action space and its application to resource management

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  • Yoshioka, Hidekazu

Abstract

The escort replicator dynamic (ERD) is a version of the replicator dynamic in evolutionary games where the utility-driven decision-making process is modulated due to the information costs to be paid by players. The escort function as a coefficient to distort the decision-making determines the behavior of solutions to the ERD, whereas its investigations are still not sufficient. Particularly, the ERD was investigated in finite-action settings in the previous studies, while that with a continuum of actions has not been studied well. In this paper, we formulate and analyze the ERD with a continuum of actions represented by a bounded interval. Our ERD is a partial integro-differential equation whose well-posedness is nontrivial because of specific nonlocal terms arising from the escort function. The Kaniadakis escort function is chosen as a major example of the escort function, with which we obtain the unique existence of solutions to the ERD. We also discuss cases with the other escort functions, such as the power and constant ones, and suggest that the growth and regularity behaviors of the escort function are crucial. Finally, we computationally apply the ERD to problems related to sustainable environmental and resource management.

Suggested Citation

  • Yoshioka, Hidekazu, 2024. "An escort replicator dynamic with a continuous action space and its application to resource management," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s096007792400537x
    DOI: 10.1016/j.chaos.2024.114985
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    1. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Alberto Bisin & Thierry Verdier, 2023. "Advances in the Economic Theory of Cultural Transmission," Annual Review of Economics, Annual Reviews, vol. 15(1), pages 63-89, September.
    3. Li, Kun & Sun, Xiaodi, 2024. "Study on taxi mode selection dynamics based on evolutionary game theory," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Nicolosi, Gabriel & Friesz, Terry & Griffin, Christopher, 2022. "Approximation of optimal control surfaces for 2 × 2 skew-symmetric evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
    6. Hu, Qi & Jin, Tao & Jiang, Yulian & Liu, Xingwen, 2024. "Reputation incentives with public supervision promote cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    7. Wang, Chao & Feng, Tian-jiao & Gao, Yan & Tao, Yi & Li, Cong, 2023. "Evolutionary stability in an eco-evolutionary game dynamics with density dependence," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Alberto Bisin & Thierry Verdier, 2022. "Advances in the Economic Theory of Cultural Transmission," NBER Working Papers 30466, National Bureau of Economic Research, Inc.
    9. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2023. "Group-size dependent synergy in heterogeneous populations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    10. Wang, Xinyu & Zhang, Shuhua & Hao, Wenwei, 2022. "Myopic vs. foresighted behaviors in a transboundary pollution game with abatement policy and emission permits trading," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    11. Biancardi, Marta & Iannucci, Gianluca & Villani, Giovanni, 2024. "Water dynamics and environmental social practice in a differential game," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    12. Ana Flávia P. Rodrigues & Igor M. Guerreiro & Charles Casimiro Cavalcante, 2018. "Deformed exponentials and portfolio selection," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-17, March.
    13. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    14. Chen, Shangrong & Bravo-Melgarejo, Sai & Mongeau, Romain & Malavolti, Estelle, 2023. "Adopting and diffusing hydrogen technology in air transport: An evolutionary game theory approach," Energy Economics, Elsevier, vol. 125(C).
    15. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
    16. Sartzetakis, Eftichios & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Environmental regulation with preferences for social status," Ecological Economics, Elsevier, vol. 209(C).
    17. Shin, Hoon C. & Vallury, Sechindra & Abbott, Joshua K. & Anderies, John M. & Yu, David J., 2022. "Understanding the effects of institutional diversity on irrigation systems dynamics," Ecological Economics, Elsevier, vol. 191(C).
    18. Pedraza, Lucía & Pinasco, Juan Pablo & Saintier, Nicolas & Balenzuela, Pablo, 2021. "An analytical formulation for multidimensional continuous opinion models," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Kaniadakis, G. & Lissia, M. & Scarfone, A.M., 2004. "Deformed logarithms and entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 41-49.
    20. Sarvesh Bandhu & Ratul Lahkar, 2023. "Evolutionary robustness of dominant strategy implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 685-721, August.
    21. Xiang Yu & Yuchong Zhang & Zhou Zhou, 2020. "Teamwise Mean Field Competitions," Papers 2006.14472, arXiv.org, revised May 2021.
    22. Shangrong Chen & Sai Bravo-Melgarejo & Romain Mongeau & Estelle Malavolti, 2023. "Adopting and diffusing hydrogen technology in air transport: An evolutionary game theory approach," Post-Print hal-04198583, HAL.
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