Minimizing Regret in Dynamic Decision Problems

TL;DR

This paper explores how the definition of menus in regret minimization affects dynamic decision-making consistency, analyzing the implications for sophisticated agents through axiomatic and example-based approaches.

Contribution

It provides a detailed analysis of menu-dependent regret minimization in dynamic settings, clarifying when dynamic consistency can be achieved.

Findings

Including forgone opportunities in the menu affects dynamic consistency.

Different menu definitions have significant implications for sophisticated regret-minimizing agents.

Axiomatic analysis clarifies conditions for dynamic consistency in regret-based decision models.

Abstract

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.