Generalized Subjective Lexicographic Expected Utility Representation

TL;DR

This paper extends the classical decision theory framework to include preferences over multiple event levels, allowing for complex risk attitudes and applications in finance and dynamic games.

Contribution

It introduces a subjective lexicographic expected utility model with infinitely many event levels, generalizing existing theories and enabling new applications.

Findings

Provides a new foundational model for decision-making under unlikely events.

Allows for infinitely many lexicographic levels of events.

Supports applications in finance and infinite dynamic games.

Abstract

We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely many lexicographically ordered levels of events and for event-dependent attitudes toward risk. Our model thus provides foundations for models in finance that rely on different attitudes toward risk (e.g. Skiadas [9]) and for off-equilibrium reasonings in infinite dynamic games, thus extending and generalizing the analysis in Blume, Brandenburger and Dekel [3].