Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Quantum-like dynamics of decision-making in prisoner's dilemma game

Masanari Asano, Irina Basieva, Andrei Yu. Khrennikov, Masanori Ohya, Yoshiharu Tanaka

Published Jan 1, 2012• 8 citations
Publisher

Abstract

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.

DOI
10.1063/1.3688998

Related papers

On Application of Gorini-Kossakowski-Sudarshan-Lindblad Equation in Cognitive Psychology

Masanari Asano, Masanori Ohya, Yoshiharu Tanaka +2 more

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.

Open Systems & Information Dynamics•Mar 1, 2011•63 citations

Quantum Theory of International Relations: Modeling Strategic Interaction with Quantum Probability Theory

Jakub Tesař

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...

•Sep 24, 2018•0 citations

Numerical Simulation of Asano-Khrennikov-Ohya Quantum-like Decision Making Model

Xingdong Zuo

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.

NeuroQuantology•Nov 21, 2014•0 citations

How Quantum Prisoner’s Dilemma Can Support Negotiations

M. Szopa

Decision-making by the two negotiating parties is simulated by a prisoner's dilemma game.The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options.Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state.The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized.On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair.We show that quantum prisoner's dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions.Some economical examples of utilizing quantum game Nash equilibria are proposed.

Optimum Economic Studies•Jan 1, 2014•6 citations

A quantum probability explanation for violations of ‘rational’ decision theory

Emmanuel M. Pothos, Jerome R. Busemeyer

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making.

Proceedings of the Royal Society B Biological Sciences•Mar 25, 2009•484 citations

A More Realistic Markov Process Model for Explaining the Disjunction Effect in One-Shot Prisoner’s Dilemma Game

Xiaoyang Xin, Mengdan Sun, Bo Liu +2 more

The quantum model has been considered to be advantageous over the Markov model in explaining irrational behaviors (e.g., the disjunction effect) during decision making. Here, we reviewed and re-examined the ability of the quantum belief–action entanglement (BAE) model and the Markov belief–action (BA) model in explaining the disjunction effect considering a more realistic setting. The results indicate that neither of the two models can truly represent the underlying cognitive mechanism. Thus, we proposed a more realistic Markov model to explain the disjunction effect in the prisoner’s dilemma game. In this model, the probability transition pattern of a decision maker (DM) is dependent on the information about the opponent’s action, Also, the relationship between the cognitive components in the evolution dynamics is moderated by the DM’s degree of subjective uncertainty (DSN). The results show that the disjunction effect can be well predicted by a more realistic Markov model. Model comparison suggests the superiority of the proposed Markov model over the quantum BAE model in terms of absolute model performance, relative model performance, and model flexibility. Therefore, we suggest that the key to successfully explaining the disjunction effect is to consider the underlying cognitive mechanism properly.

Mathematics•Mar 6, 2022•1 citation
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.
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.
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...
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.
Decision-making by the two negotiating parties is simulated by a prisoner's dilemma game.The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options.Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state.The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized.On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair.We show that quantum prisoner's dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions.Some economical examples of utilizing quantum game Nash equilibria are proposed.
Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making.
The quantum model has been considered to be advantageous over the Markov model in explaining irrational behaviors (e.g., the disjunction effect) during decision making. Here, we reviewed and re-examined the ability of the quantum belief–action entanglement (BAE) model and the Markov belief–action (BA) model in explaining the disjunction effect considering a more realistic setting. The results indicate that neither of the two models can truly represent the underlying cognitive mechanism. Thus, we proposed a more realistic Markov model to explain the disjunction effect in the prisoner’s dilemma game. In this model, the probability transition pattern of a decision maker (DM) is dependent on the information about the opponent’s action, Also, the relationship between the cognitive components in the evolution dynamics is moderated by the DM’s degree of subjective uncertainty (DSN). The results show that the disjunction effect can be well predicted by a more realistic Markov model. Model comparison suggests the superiority of the proposed Markov model over the quantum BAE model in terms of absolute model performance, relative model performance, and model flexibility. Therefore, we suggest that the key to successfully explaining the disjunction effect is to consider the underlying cognitive mechanism properly.