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Decision making in stochastic extensive form II: Stochastic extensive forms and games

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  • E. Emanuel Rapsch

Abstract

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.

Suggested Citation

  • E. Emanuel Rapsch, 2024. "Decision making in stochastic extensive form II: Stochastic extensive forms and games," Papers 2411.17587, arXiv.org.
    • Handle: RePEc:arx:papers:2411.17587
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