A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917594856947712 |
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| author | Yoshioka, Hidekazu Tsujimura, Motoh Yoshioka, Yumi |
| author_facet | Yoshioka, Hidekazu Tsujimura, Motoh Yoshioka, Yumi |
| contents | 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un-der uncertainty is generalized to the dynamic where the exponential function for the softmax part has been replaced by a rational one that includes the former as a special case.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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation Yoshioka, Hidekazu Tsujimura, Motoh Yoshioka, Yumi Dynamical Systems Systems and Control 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un-der uncertainty is generalized to the dynamic where the exponential function for the softmax part has been replaced by a rational one that includes the former as a special case.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. |
| title | A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation |
| topic | Dynamical Systems Systems and Control |
| url | https://arxiv.org/abs/2402.13453 |