Projective Expected Utility

TL;DR

This paper introduces a projective generalization of expected utility inspired by quantum mechanics, resolving classic decision paradoxes while maintaining simplicity and ensuring equilibrium existence in finite games.

Contribution

It presents a novel decision theory framework that generalizes expected utility using projective methods, addressing longstanding paradoxes in decision theory.

Findings

Resolves classic decision paradoxes

Ensures equilibrium existence in finite games

Retains simplicity and tractability

Abstract

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.