Partially Identified Ambiguity

TL;DR

This paper develops a theory of learning under ambiguity, extending classical Bayesian results, and applies it to robust analysis, persuasion games, and decision-making with ambiguous beliefs.

Contribution

It introduces a framework where classical Bayesian results extend to ambiguity, clarifies time inconsistency in robust analysis, and offers a benchmark for communication under ambiguity.

Findings

Experiments are equivalent to distributions over posterior beliefs.

Blackwell's order coincides with more informative and more valuable orders.

Provides a natural benchmark for communication under ambiguity.

Abstract

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning extend to the setting with ambiguity: experiments are equivalent to distributions over posterior beliefs, and Blackwell's more informative and more valuable orders coincide. When applied to the setting of robust Bayesian analysis, our results clarify the source of time inconsistency in the Gamma-minimax problem and provide an argument in favor of the conditional Gamma-minimax criterion. We also apply our results to a persuasion game to illustrate that our model provides a natural benchmark for communication under ambiguity.