Envelopes of conditional probabilities extending a strategy and a prior probability

TL;DR

This paper studies how strategies and prior probabilities can be extended to full conditional probabilities, providing a closed-form expression for their envelopes and characterizing subclasses with additional properties.

Contribution

It introduces a novel analysis of the extension class of strategies and priors, offering explicit envelope formulas and topological characterizations of subclasses.

Findings

Closed-form expressions for envelopes of extensions

Topological characterization of subclasses with disintegrability and conglomerability

Analysis of non-uniqueness in extending strategies and priors

Abstract

Any strategy and prior probability together are a coherent conditional probability that can be extended, generally not in a unique way, to a full conditional probability. The corresponding class of extensions is studied and a closed form expression for its envelopes is provided. Then a topological characterization of the subclasses of extensions satisfying the further properties of full disintegrability and full strong conglomerability is given and their envelopes are studied.