Application to Decision Making Theory and Cognitive Science

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.