We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology — the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1, 2], Croson [3], Hofstader [4, 5] demonstrated that in general real players do not use "rational strategy" provided by classical game theory; this psychological phenomenon was called the disjunction effect. We elaborate a model of quantum-like decision making which can explain this effect ("irrationality" of plays). Our model is based on quantum information theory. The main result of this paper is the derivation of Gorini-Kossakowski-Sudarshan-Lindblad equation whose equilibrium solution gives the quantum state used for decision making. It is the first application of this equation in cognitive psychology.
We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology — the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1, 2], Croson [3], Hofstader [4, 5] demonstrated that in general real players do not use "rational strategy" provided by classical game theory; this psychological phenomenon was called the disjunction effect. We elaborate a model of quantum-like decision making which can explain this effect ("irrationality" of plays). Our model is based on quantum information theory. The main result of this paper is the derivation of Gorini-Kossakowski-Sudarshan-Lindblad equation whose equilibrium solution gives the quantum state used for decision making. It is the first application of this equation in cognitive psychology.
In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.
In classical game theory, the rational behavior for the player is to make the decision which is approaching Nash equilibrium. The Prisoner's Dilemma, which is a canonical game, is often used to present the rationality. In real experiment in cognitive psychology which were performed by Tversky and Shafir, the statistical data show the existence of the irrational behaviors in reality. The phenomenon is called disjunction effect. To explain why it probably happens, we review the Asano-Khrennikov-Ohya model which is the mathematical modeling of the process of decision making in the game of Prisoner's Dilemma. It applies only the mathematical apparatus of quantum mechanics to the decision making process rather than the quantum physical model. In this paper, we present several numerical simulations for the Asano-Khrennikov-Ohya model together with the graphs of the von Neumann entropy for the solutions. By analyzing the simulation results, we explicitly and numerically present the existence of the irrational behavior for the player which is generated by the Asano-Khrennikov-Ohya model.
Recent results from cognitive psychology suggest that human behavior can be, in some situations, better described by laws known from physical quantum theory. This work responds to this development and seeks to answer the question of how quantum models of cognition and decision-making can contribute to our understanding of the social world. We introduce the approaches to the application of quantum theory in social sciences - quantum consciousness, quantum reasoning and quantum metaphor and further develop the second, in the context of strategic interaction in game theory. We show that the quantum model corresponds to both the psychological intuition and many empirically known anomalies such as the order effect, disjunction effect, or context effect. In this work, we derive a specific model of strategic interaction between two players, and we test it in the experimental Prisoner's Dilemma game. The model is based on the rational choice theory, which is nevertheless re-defined when it is shown how the strategic choice is changed if the quantum probability (C*-algebra) is used as the underlying theory instead of classical probability (σ-algebra). The results obtained support the quantum model and showed a different representation of the game among various groups of players. The quantum model of...
This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.
This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.
We show that (in contrast to rather common opinion) the domain of applications of the mathematical formalism of quantum mechanics is not restricted to physics. This formalism can be applied to the description of various quantum-like (QL) information processing. In particular, the calculus of quantum (and more general QL) probabilities can be used to explain some paradoxical statistical data which was obtained in psychology and cognitive science. We consider the QL description of prisoners dilemma (PD) and so called disjunction effect (violation of Savage's sure thing principle which plays the fundamental role in modern economics).