Abstract
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?.
Highlights
The quantum games and the quantum computer are closely-related
One application of the uncertainty principle in Time Series is related to Spectral Analysis “The more precisely the random variable VALUE is determined, the less precisely the frequency VALUE is known at this instant, and ”
A complete relationship exists between Quantum Mechanics and Game Theory
Summary
The quantum games and the quantum computer are closely-related. The science of Quantum Computer is one of the modern paradigms in Computer Science and Game Theory [5,6,7,8, 23, 41, 42, 53]. Several recently proposed quantum information application theories can already be conceived as competitive situations, where several factors which have opposing motives interact These parts may apply quantum operations using bipartite quantum systems. On the other hand, generalizing decision theory in the domain of quantum probabilities seems interesting, as the roots of game theory are partly rooted in probability theory [43, 44] In this context it is of interest to investigate what solutions are attainable if superpositions of strategies are allowed [18, 41, 42, 50, 51, 57]. One application of the uncertainty principle in Time Series is related to Spectral Analysis “The more precisely the random variable VALUE is determined, the less precisely the frequency VALUE is known at this instant, and ”. This paper is organized as follows: Section 2: Quantum Games and Hermite’s Polynomials, Section 3: Time Series and Heisenberg’s Principle, Section 4: Applications of the Models, and Section 5: Conclusion
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