Mathematical Topics on Representations of Ordered Structures and Utility Theory

This book offers an essential review of central theories, current research and applications in the field of numerical representations of ordered structures. It is intended as a tribute to Professor Ghanshyam B. Mehta, one of the leading specialists on the numerical representability of ordered structures, and covers related applications to utility theory, mathematical economics, social choice theory and decision-making. Taken together, the carefully selected contributions provide readers with an authoritative review of this research field, as well as the knowledge they need to apply the theories and methods in their own work.

Contenu

Topology and preference relations.- The existence and the non-existence of utility functions.- Open questions in Utility Theory.- Representations of interval orders on connected separable.- Searching for a Debreu's open gap lemma for semiorders.- A note on Candeal and Indurain's semiorder separability.- Chain Representations of Nested Families of Biorders.- A note on representable group topologies.- Preferences in abstract convex structures.- Strictly monotonic preferences.- Continuity and continuous multi-utility representations.- Jointly continuous multy-utility representation.- Subjective States without the Completeness Axiom.- Preference for Flexibility: A Continuous Representation.- The Arrow-Hahn Construction in a locally compact.- Continuous Utility Representation of Fuzzy Preferences.- Similarity relation by using money-metric utility functions.- The interplay between intergenerational justice.- Comparative Risk Aversion for State-Dependent Preferences.