Quantum-Like Model for Decision Making Process in Two Players Game

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999).

[1]  Masanori Ohya,et al.  On compound state and mutual information in quantum information theory , 1983, IEEE Trans. Inf. Theory.

[2]  A. Khrennikov.  Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena , 2004 .

[3]  Andrei Khrennikov.  Interference of probabilities in the classical probabilistic framework , 2005, Fuzzy Sets Syst..

[4]  Masanori Ohya,et al.  Some aspects of quantum information theory and their applications to irreversible processes , 1989 .

[5]  Masanori Ohya,et al.  Compound Channels, Transition Expectations, and Liftings , 1999 .

[6]  Masanori Ohya,et al.  Note on quantum probability , 1983 .

[7]  Massanori Ohya.  State change and entropies in quantum dynamical systems , 1985 .

[8]  Masanori Ohya,et al.  Quantum ergodic channels in operator algebras , 1981 .

[9]  A. Tversky,et al.  Thinking through uncertainty: Nonconsequential reasoning and choice , 1992, Cognitive Psychology.

[10]  N. David Mermin,et al.  Boojums All The Way Through , 1990 .

[11]  Andrei Khrennikov.  Quantum-Like models for decision making in psychology and cognitive science , 2009 .

[12]  Andrei Khrennikov,et al.  Quantum-like brain: "Interference of minds". , 2006, Bio Systems.

[13]  Andrei Khrennikov,et al.  The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics , 2005 .

[14]  A. Tversky,et al.  The Disjunction Effect in Choice under Uncertainty , 1992 .