Modified Asano-Ohya-Khrennikov quantum-like model for decision-making process in a two-player game with nonlinear self-
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Modified Asano-Ohya-Khrennikov quantum-like model for decision-making process in a two-player game with nonlinear self- and cross-interaction terms of brain’s amygdala and prefrontal-cortex Luluk Muthoharoh 1 & Hendradi Hardhienata 1 & Husin Alatas 1 Received: 13 January 2020 / Accepted: 24 June 2020/ # Springer Nature B.V. 2020
Abstract
In this report, we propose a modification on the Asano-Ohya-Khrennikov quantum-like decision-making process model of a two-player game by adding additional nonlinear terms to the related comparison step dynamical equation. The additions are in the form of a self-interaction and cross-interaction of the brain’s amygdala and prefrontal cortex. We show that the cross-interaction significantly determines the final decision of a player, whether it becomes a rational or an irrational choice. In contrast, the nonlinear selfinteraction term provides a feedback mechanism that speeds up the corresponding decision-making process. We also suggest the form of expectation values of the overall reaction rate coefficients of those nonlinear terms by making an analogy with the original model formulation. Keywords Asano-Ohya-Khrennikov quantum-like model . Decision-making process . Twoplayer game . Amygdala . Prefrontal cortex
1 Introduction The physical mechanism underlying the high complexity of human brain behavior undoubtedly has attracted much attention in recent years [1, 2]. Mathematical and computational models have been proposed to explain some particular brain’s behaviors [3–5]. One of those behaviors is the ability to decide on a specific situation, e.g., when two persons play a specific game. Players will take actions that are increasing their payoffs in order to win the game. For the rational players, if there is an appropriate action which can be decided uniquely, they will choose it with a probability of 1, without considering the action of other players. On the other * Husin Alatas [email protected]
1
Theoretical Physics Division, Department of Physics, IPB University (Bogor Agricultural University), Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Indonesia
L. Muthoharoh et al.
hand, for irrational players, this situation does not automatically lead them to decide uniquely or in other words, which actions they will take are probabilistic. Shafir and Tversky [6] have shown from their experiment in two-player prisoner’s dilemma (PD) game that the probability of a player to choose action irrationally is 0.37. In [7], Asano, Ohya, and Khrennikov have developed a model to describe the behavior of such player’s rational/irrational choices in a two-player game. Their model formulation borrowed the quantum theory technical description, where each of the players is represented by state vectors, which are called “predictive state” and “mental state,” as elements of a 4dimensional Hilbert space. The basic assumption of their quantum-like model was the independency of each player choices, where a player does not know the choice of the other player and can only make predictions on it. T
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