APPLIED & INTERDISCIPLINARY MATHEMATICS | RESEARCH ARTICLE Games of entangled agents

1 * Abstract: The paper extends the mathematical formalism of quantum physics to include games of intelligent agents that communicate due to entanglement. The novelty of the approach is based upon a human factor-based behavioral model of an intelligent agent. The model is quantum inspired: it is represented by a modified Madelung equation in which the gradient of quantum potential is replaced by a specially chosen information force. It consists of motor dynamics simulating actual behavior of the agent, and mental dynamics representing evolution of the corresponding knowledge base and incorporating this knowledge in the form of information flows into the motor dynamics. Due to feedback from mental dynam- ics, the 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; each agent is entangled (in a quantum way) to other agents and makes calculated predictions for future actions; human factor is associated with violation of the second law of thermodynamics: the system can move from disorder to order without external help, and that represents intrinsic intelligence. All of these departures actually extend and complement the classical methods making them especially successful in analysis of communications of agents represented by new mathematical formalism, and in particular, in agent- based economics with a human factor.