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

Abstract

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 Shafir and Tversky Tversky, 1992a, 1992b), 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 (Asano et al., 2011c;Khrennikov, 2011b) 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-KhrennikovOhya 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.

Financial Market Modeling with Quantum Neural Networks

“…The quantum-based approach goes, however, beyond a good match to price dynamics and turbulence modeling. The growing empirical evidence of quantum interference signatures in human cognition, when faced with decision problems, has led to the development of a Quantum Theory-based Cognitive Science forming a theoretical ground for Econophysics modeling, with strong implications for Finance (Busemeyer and Franco, 2010;Busemeyer and Bruza, 2012;Wang and Busemeyer, 2013;Busemeyer and Wang, 2014;Haven and Khrennikov, 2013;Zuo, 2014;Khrennikov and Basieva, 2014).…”

“…The main research problem regarding Quantum Theory-based Cognitive Science applied to Finance can be expressed as follows: if there is emprical support to the fact that human cognition, in decision problems, leads to a decision behavior computationally isomorphic to quantum adaptive computation (Busemeyer and Franco, 2010;Busemeyer and Bruza, 2012;Wang and Busemeyer, 2013;Busemeyer and Wang, 2014;Zuo, 2014;Khrennikov and Basieva, 2014;Gonçalves, 2015), then, the modeling of financial market dynamics needs to work with models of behavior that incorporate, in their probabilistic description, quantum interference terms Haven and Khrennikov, 2013).…”