Minimizing Regret in Dynamic Decision Problems
This work addresses theoretical subtleties in decision theory for researchers, but it appears incremental as it builds on existing regret-minimization frameworks without introducing a new paradigm.
The paper tackles the problem of applying regret-minimization to dynamic decision problems by examining how to define menus, including forgone opportunities, to ensure dynamic consistency and handle sophistication. It characterizes conditions for consistency and explores implications through axiomatic analysis and examples.
The menu-dependent nature of regret-minimization creates subtleties when it is applied to dynamic decision problems. Firstly, it is not clear whether \emph{forgone opportunities} should be included in the \emph{menu}, with respect to which regrets are computed, at different points of the decision problem. If forgone opportunities are included, however, we can characterize when a form of dynamic consistency is guaranteed. Secondly, more subtleties arise when sophistication is used to deal with dynamic inconsistency. In the full version of this paper, we examine, axiomatically and by common examples, the implications of different menu definitions for sophisticated, regret-minimizing agents.