Optimal Mechanism in a Dynamic Stochastic Knapsack Environment
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914689091371008 |
|---|---|
| author | Jung, Jihyeok Song, Chan-Oi Lee, Deok-Joo Yoon, Kiho |
| author_facet | Jung, Jihyeok Song, Chan-Oi Lee, Deok-Joo Yoon, Kiho |
| contents | This study introduces an optimal mechanism in a dynamic stochastic knapsack environment. The model features a single seller who has a fixed quantity of a perfectly divisible item. Impatient buyers with a piece-wise linear utility function arrive randomly and they report the two-dimensional private information: marginal value and demanded quantity. We derive a revenue-maximizing dynamic mechanism in a finite discrete time framework that satisfies incentive compatibility, individual rationality, and feasibility conditions. It is achieved by characterizing buyers' utility and deriving the Bellman equation. Moreover, we propose the essential penalty scheme for incentive compatibility, as well as the allocation and payment policies. Lastly, we propose algorithms to approximate the optimal policy, based on the Monte Carlo simulation-based regression method and reinforcement learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Mechanism in a Dynamic Stochastic Knapsack Environment Jung, Jihyeok Song, Chan-Oi Lee, Deok-Joo Yoon, Kiho Computer Science and Game Theory General Economics Economics This study introduces an optimal mechanism in a dynamic stochastic knapsack environment. The model features a single seller who has a fixed quantity of a perfectly divisible item. Impatient buyers with a piece-wise linear utility function arrive randomly and they report the two-dimensional private information: marginal value and demanded quantity. We derive a revenue-maximizing dynamic mechanism in a finite discrete time framework that satisfies incentive compatibility, individual rationality, and feasibility conditions. It is achieved by characterizing buyers' utility and deriving the Bellman equation. Moreover, we propose the essential penalty scheme for incentive compatibility, as well as the allocation and payment policies. Lastly, we propose algorithms to approximate the optimal policy, based on the Monte Carlo simulation-based regression method and reinforcement learning. |
| title | Optimal Mechanism in a Dynamic Stochastic Knapsack Environment |
| topic | Computer Science and Game Theory General Economics Economics |
| url | https://arxiv.org/abs/2402.14269 |