A model of adaptive decision making from representation of information environment by quantum fields

Abstract

We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are of the purely informational nature. The QFT-model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism (QBism). We demonstrate the quantum-like interference effect in DM which is exhibited as a violation of the formula of total probability and hence the classical Bayesian inference scheme.

arXiv commentin press in Philosophical Transactions A

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• One-directional quantum mechanical dynamics and an application to decision making
• A dynamical approach to compatible and incompatible questions