The Quantum Foundations of Utility : Resolving the Incompleteness of Economic Theory

We define the axioms of quantum game theory and show that classical, Nashian, game theory is a special case of quantum game theory. In our more general framework, we prove the insufficiency of the von Neumann Morgenstern utility, because it is not uniquely defined. Relating utility to the time evolution of strategies, we show that utility can be uniquely defined by the Hamiltonian operator. Under Rawls' "veil of ignorance" and "first principle of justice", we show that utility, at the classical limit, is canonically distributed. The entropy functional is derived and related to the utility functional through the canonical economic ensemble. Four absolute and limiting economic laws are derived from the entropy functional and the definition of statistical equilibrium. The entropy functional is then extended to macroeconomics, replacing traditional production functions that neglect entropy. Finally, the Allais and Ellsberg paradoxes are resolved using the derived Helmholtz potential as the metric for classical choice under uncertainty