A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation
<|reference_start|>A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation: The classical logit dynamic on a continuous action space for decision-making un-der uncertainty is generalized to the dynamic where the exponential function for the softmax part has been replaced by a rational one that includes the former as a special case. We call the new dynamic as the rational logit dynamic. The use of the rational logit function implies that the uncertainties have a longer tail than that assumed in the classical one. We show that the rational logit dynamic admits a unique measure-valued solution and the solution can be approximated using a fi-nite difference discretization. We also show that the vanishing-noise limit of the rational logit dynamic exists and is different from the best-response one, demon-strating that influences of the uncertainty tail persist in the rational logit dynamic. We finally apply the rational logit dynamic to a unique fishing competition data that has been recently acquired by the authors.<|reference_end|>
@article{yoshioka2024a,
    title={A rational logit dynamic for decision-making under uncertainty:
  well-posedness, vanishing-noise limit, and numerical approximation},
    author={Hidekazu Yoshioka, Motoh Tsujimura, and Yumi Yoshioka},
    journal={arXiv preprint arXiv:2402.13453},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.13453},
    primaryClass={math.DS cs.SY eess.SY}
}