Application to Decision Making Theory and Cognitive Science

  • Masanari Asano
  • Andrei Khrennikov
  • Masanori Ohya
  • Yoshiharu Tanaka
  • Ichiro Yamato
Chapter
First Online:

Abstract

In this chapter the formalism of quantum probability and quantum information theory (in its generalized form based on theory of lifting) is applied to construct the QL-representations for cognitive processes, especially decision making in games of the prisoner’s dilemma type. Our modeling is based on the results of extended studies in the domain of cognitive psychology demonstrated that in some mental contexts players behave irrationally, i.e., they select mixed strategies which are different from the Nash equilibrium predicted by classical game theory. The simplest model of such irrational behavior is based on theory of open quantum systems and quantum master equation. More complex cognitive situations are modelled with aid quantum adaptive dynamics generalizing theory of open quantum systems. We also construct the QL-representation for bistable perception. We are able to construct quantum operators providing the adequate operational description of know statistical data. To check nonclassicality of these data we use a Bell-type inequality, namely, the Leggett-Garg inequality.

Keywords

Cognitive processes Decision making Games of prisoner’s dilemma type Irrational behavior Nash equilibrium Bistable perception Open quantum systems Adaptive quantum dynamics Bell inequality Leggett-Garg inequality 
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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Masanari Asano
    • 1
  • Andrei Khrennikov
    • 2
  • Masanori Ohya
    • 3
  • Yoshiharu Tanaka
    • 3
  • Ichiro Yamato
    • 4
  1. 1.Liberal Arts DivisionTokuyama College of TechnologyTokuyamaJapan
  2. 2.International Center for Mathematical Modeling in Physics and Cognitive ScienceLinnaeus UniversityVäxjöSweden
  3. 3.Information ScienceTokyo University of ScienceTokyoJapan
  4. 4.Department of Biological Science and TechnologyTokyo University of ScienceTokyoJapan

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