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 Tversky and Shafir, 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 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-Khrennikov-Ohya 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.