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Uncertainty measurement with belief entropy on the interference effect in the quantum-like Bayesian networks. (English) Zbl 1429.91107

Summary: The Bayesian Network is a kind of probabilistic graphical models, having been applied to various fields for inference and learning. A quantum-like Bayesian Network has been proposed to model the prisoner’s dilemma, the famous example of social dilemma games. Recent findings reveal that people’s behaviors violate the Sure Thing Principle in such games. The quantum-like Bayesian network considers the people’s behaviors as wave functions and explains the violation as the interference effect. The determination of the interference effect is an essential part of modeling the Bayesian network.
In this paper, a belief entropy based uncertainty measurement is proposed to quantify the interference effect. Unlike most other methods, the measurement is a total unsupervised process, making the model predictive. On the other hand, the belief entropy based method provides a potential physical explanation of the interference effect. Tested with empirical data, the proposed method is proved to be precise to quantify the interference effect. The results further verify that the quantum-like Bayesian network is a delightful way to accommodate the paradoxical findings in social dilemma games.

MSC:

91B06 Decision theory
81P15 Quantum measurement theory, state operations, state preparations
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
62B10 Statistical aspects of information-theoretic topics
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