Dynamic consistency of expected utility under non-classical (quantum) uncertainty

TL;DR

This paper develops a quantum-based expected utility theory for decision-making under non-classical uncertainty, introducing quantum lotteries and axioms, and explores dynamic consistency and its implications in behavioral economics.

Contribution

It introduces a novel quantum utility framework with axioms and representation theorem, linking dynamic consistency to the von Neumann-Lüders postulate in decision theory.

Findings

Quantum lotteries extend classical decision models.

Dynamic consistency relates to quantum belief updating.

Potential applications in behavioral economics and persuasion.

Abstract

Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neuman-L\"uders postulate applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion.