Weighted Garbling
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914383341289472 |
|---|---|
| author | Kim, Daehyun Obara, Ichiro |
| author_facet | Kim, Daehyun Obara, Ichiro |
| contents | We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the former. We show that this is equivalent to ordinary garbling conditional on a payoff-irrelevant event. We also characterize the order in terms of induced posterior belief distributions, showing that it depends only on their support. Our main results provide two decision-theoretic characterizations of this order. First, in static decision problems, one experiment dominates another if and only if its value of information is at least a fixed fraction of the other's across all problems. Second, in a class of stopping time problems with a hidden Markov process and repeated experimentation, one experiment dominates another if and only if it yields weakly higher expected payoffs for every problem with a regular prior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Garbling Kim, Daehyun Obara, Ichiro Theoretical Economics We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the former. We show that this is equivalent to ordinary garbling conditional on a payoff-irrelevant event. We also characterize the order in terms of induced posterior belief distributions, showing that it depends only on their support. Our main results provide two decision-theoretic characterizations of this order. First, in static decision problems, one experiment dominates another if and only if its value of information is at least a fixed fraction of the other's across all problems. Second, in a class of stopping time problems with a hidden Markov process and repeated experimentation, one experiment dominates another if and only if it yields weakly higher expected payoffs for every problem with a regular prior. |
| title | Weighted Garbling |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2410.21694 |