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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.

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  • 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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