Quantum Financial Economics of Games of Strategy and Financial Decisions

TL;DR

This paper introduces a quantum financial framework for strategic games, extending Nash's theorem to include financial decision-making and market interactions, enabling Pareto optimal outcomes without market completeness.

Contribution

It extends Nash's theorem to quantum financial settings, linking strategic games with financial markets and deriving quantum Arrow-Debreu prices without requiring market completeness.

Findings

Quantum Nash equilibrium yields complete Arrow-Debreu prices.

Pareto optimal results achieved without securities market completeness.

Entanglement of strategic and financial decisions demonstrated.

Abstract

A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure exchange economies and the finite-state securities market optimization problem, thus addressing, within the financial setting, the interplay between companies' business games and financial agents' behavior. A complete set of quantum Arrow-Debreu prices, resulting from the game of strategy's quantum Nash equilibrium, is shown to hold, even in the absence of securities' market completeness, such that Pareto optimal results are obtained without having to assume the completeness condition that the rank of the securities' payoff matrix is equal to the number of alternative lottery states.