Quantum games entropy

Edward Jiménez

Edward Jiménez

This paper introduces Hermite's polynomials, in the description of quantum games. Hermite's polynomials are associated with gaussian probability density. The gaussian probability density represents minimum dispersion. I introduce the concept of minimum entropy as a paradigm of both Nash's equilibrium (maximum utility MU) and Hayek equilibrium (minimum entropy ME). The ME concept is related to Quantum Games. Some questions arise after carrying out this exercise: i) What does Heisenberg's uncertainty principle represent in Game Theory and Time Series?, and ii) What do the postulates of Quantum Mechanics indicate in Game Theory and Economics?.

Esteban Guevara Hidalgo

The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.

Kolokoltsov Vasili

Alexis R. Legón, Ernesto A. Medina

Classical games get fundamentally modified in the quantum realm because of non-locality and entanglement, that bypass some of the crucial features of the classical problem that define a dilemma. We will analyze how the dilemma can be shunted and even completely eliminated by the players using quantum strategies from the viewpoint of joint probabilities. In this approach, the game information (entropy) needs to be incorporated into the game strategies. We also connect the potential of the formalism of quantum games with the transmission of quantum information in quantum noisy channels and recent considerations of the connection between thermalization mechanisms in statistical mechanics, the many body problem and cooperative games considered here in the quantum regime.

Παναγιώτης Αποστολίδης, Εύαγγελος Κ. Κοντονικολάου