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Dynamical free energy based model for quantum decision making

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  • Tanaka, Shigenori
  • Umegaki, Toshihito
  • Nishiyama, Akihiro
  • Kitoh-Nishioka, Hirotaka

Abstract

We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.

Suggested Citation

  • Tanaka, Shigenori & Umegaki, Toshihito & Nishiyama, Akihiro & Kitoh-Nishioka, Hirotaka, 2022. "Dynamical free energy based model for quantum decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    • Handle: RePEc:eee:phsmap:v:605:y:2022:i:c:s0378437122006161
    DOI: 10.1016/j.physa.2022.127979
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    References listed on IDEAS

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    1. Hameroff, Stuart & Penrose, Roger, 1996. "Orchestrated reduction of quantum coherence in brain microtubules: A model for consciousness," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 40(3), pages 453-480.
    2. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, September.
    3. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
    4. Nishiyama, Akihiro & Tanaka, Shigenori & Tuszynski, Jack A., 2021. "Non-equilibrium Quantum Brain Dynamics II: Formulation in 3+1 dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. Vyacheslav I. Yukalov & Didier Sornette, 2008. "Mathematical Basis of Quantum Decision Theory," Swiss Finance Institute Research Paper Series 08-25, Swiss Finance Institute.
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