Results about sets of desirable gamble sets
This work addresses foundational issues in decision theory for AI and economics, but it appears incremental as it builds on existing models without introducing new paradigms.
The paper tackles the problem of modeling agents' opinions and choice preferences under uncertainty using coherent sets of desirable gamble sets, providing results on coherence axioms, natural extension, and representation by a proper filter of coherent sets of desirable gambles.
Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension of a given set of desirable gamble sets. We also show that coherent sets of desirable gamble sets can be represented by a proper filter of coherent sets of desirable gambles.