Decision making in stochastic extensive form II: Stochastic extensive forms and games
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916496746217472 |
|---|---|
| author | Rapsch, E. Emanuel |
| author_facet | Rapsch, E. Emanuel |
| contents | A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional "nature" agent, this framework uses a single lottery draw to select a tree of a given decision forest. Each "personal" agent receives dynamic updates from an own oracle on the lottery outcome and makes partition-refining choices adapted to this information. This theory addresses a key limitation of existing approaches in extensive form theory, which struggle to model continuous-time stochastic processes, such as Brownian motion, as outcomes of "nature" decision making. Additionally, a class of stochastic extensive forms based on time-indexed action paths is constructed, encompassing a wide range of models from the literature and laying the groundwork for an approximation theory for stochastic differential games in extensive form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decision making in stochastic extensive form II: Stochastic extensive forms and games Rapsch, E. Emanuel Theoretical Economics Optimization and Control Probability 91A15 (Primary) 91A18, 91B06 (Secondary) A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional "nature" agent, this framework uses a single lottery draw to select a tree of a given decision forest. Each "personal" agent receives dynamic updates from an own oracle on the lottery outcome and makes partition-refining choices adapted to this information. This theory addresses a key limitation of existing approaches in extensive form theory, which struggle to model continuous-time stochastic processes, such as Brownian motion, as outcomes of "nature" decision making. Additionally, a class of stochastic extensive forms based on time-indexed action paths is constructed, encompassing a wide range of models from the literature and laying the groundwork for an approximation theory for stochastic differential games in extensive form. |
| title | Decision making in stochastic extensive form II: Stochastic extensive forms and games |
| topic | Theoretical Economics Optimization and Control Probability 91A15 (Primary) 91A18, 91B06 (Secondary) |
| url | https://arxiv.org/abs/2411.17587 |