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Quantum-like dynamics of decision-making

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  • Asano, Masanari
  • Basieva, Irina
  • Khrennikov, Andrei
  • Ohya, Masanori
  • Tanaka, Yoshiharu

Abstract

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect (“irrationality” of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011) [55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker.

Suggested Citation

  • Asano, Masanari & Basieva, Irina & Khrennikov, Andrei & Ohya, Masanori & Tanaka, Yoshiharu, 2012. "Quantum-like dynamics of decision-making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2083-2099.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:5:p:2083-2099
    DOI: 10.1016/j.physa.2011.11.042
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    2. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    3. Luke Snow & Shashwat Jain & Vikram Krishnamurthy, 2022. "Lyapunov based Stochastic Stability of Human-Machine Interaction: A Quantum Decision System Approach," Papers 2204.00059, arXiv.org.
    4. Di Salvo, Rosa & Gorgone, Matteo & Oliveri, Francesco, 2020. "Generalized Hamiltonian for a two-mode fermionic model and asymptotic equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Charles-Cadogan, G., 2021. "Utility Representation in Abstract Wiener Space," CRETA Online Discussion Paper Series 70, Centre for Research in Economic Theory and its Applications CRETA.
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    7. Bagarello, F., 2020. "One-directional quantum mechanical dynamics and an application to decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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