Quantum-like model for decision making process in Two players game. A non-Kolmogorovian model. (English) Zbl 1211.81004
Summary: In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of A. Khrennikov [Information dynamics in cognitive, psychological and anomalous phenomena. Fundamental Theories of Physics, Fundamental Theories of Physics 138. Boston, MA: Kluwer Academic Publishers (2004); Fuzzy Sets Syst. 155, No. 1, 4–17 (2005); Biosystems 84, 225–241 (2006); Found. Phys. 35, No. 10, 1655–1693 (2005; Zbl 1102.81008); in QP-PQ Quantum Probability and White Noise Analysis 24, 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 [L. Accardi and M. Ohya, Appl. Math. Optimization 39, No. 1, 33–59 (1999; Zbl 0941.94011)].
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 81Q65 | Alternative quantum mechanics (including hidden variables, etc.) |
| 91A05 | 2-person games |
| 62C86 | Statistical decision theory and fuzziness |
| 90C40 | Markov and semi-Markov decision processes |
References:
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