Psychological games of entangled players

TL;DR

This paper presents a novel quantum-inspired model of entangled players in differential games, where mental and motor dynamics influence each other, leading to quantum-like behavior in decision-making processes.

Contribution

It introduces a non-Newtonian, quantum-inspired formalism for modeling entangled players, incorporating mental and motor dynamics with feedback mechanisms.

Findings

Model exhibits quantum-like trajectories due to mental feedback.

Entanglement correlates action probabilities, not actions themselves.

New approach to differential games with living agents' behavior.

Abstract

The paper introduces a new approach to theory of differential games in which entangled players try to predict and influence actions of their adversaries. The entanglement is generated be a joint probability density known by the players. Incase of complex density, its imaginary part represents a measure of uncertainty of the density distribution. The novelty of the approach is in non-Newtonian mathematical formalism thatis based upon a behavioral model of Livings. The model is quantum-inspired: it represented by a modified Madelung equation which the quantum potential is replaced by different, specially chosen "computational" potential. It consists of motor dynamics simulating actual behavior of the object, and mental dynamics representing evolution of the corresponding knowledge-based and incorporating this knowledge in the for m of information flows into the motor dynamics. Due to feedback from mental dynamics, motor dynamics attains quantum-like properties: its trajectory splits into a family of different trajectories, and each of those trajectories can be chosen with the probability prescribed by the mental dynamics. The model addresses a new type of entanglement that correlates the probabilities of actions of Livings rather than the actions themselves.