Quantum Financial Economics of Games of Strategy and Financial Decisions

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.

Keywords: quantum financial economics, finite games, quantum nash equilibrium, quantum arrow-debreu prices, securities markets

JEL Classification: G00, G30, G12, C70, C72