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The quantum foundations of utility and value.

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  • 1Signal Power and Light, Inc, Cordova, AL, USA.

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This study generalizes game theory using quantum mechanics, revealing classical game theory as a special case. It establishes the equivalence of von Neumann entropy and utility, with the Hamiltonian operator representing value.

Keywords:
entropygame theoryquantum theoryutilityvalue

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Area of Science:

  • Quantum mechanics
  • Game theory
  • Thermodynamics

Background:

  • Classical game theory lacks a unified framework for utility and value.
  • Quantum mechanics offers novel mathematical formalisms.

Purpose of the Study:

  • To generalize classical game theory using quantum formalism.
  • To establish new perspectives on utility and value.
  • To explore the connection between thermodynamics and social sciences.

Main Methods:

  • Application of quantum formalism to game theory.
  • Mathematical proof of classical game theory as a special case of quantum game theory.
  • Analysis of von Neumann entropy and von Neumann-Morgenstern utility.

Main Results:

  • Quantum game theory is a generalization of classical game theory.
  • Von Neumann entropy is equivalent to von Neumann-Morgenstern utility.
  • The Hamiltonian operator represents value in this framework.

Conclusions:

  • Quantum formalism provides a more comprehensive framework for game theory.
  • This work bridges quantum mechanics, economics, and thermodynamics.
  • The findings offer new insights into decision-making and value representation.