Quantum Cournot model based on general entanglement operator

TL;DR

This paper investigates a quantum Cournot duopoly model using a general entanglement operator with quadratic terms, analyzing how entanglement and phase parameters influence Nash equilibrium payoffs.

Contribution

It introduces a comprehensive quantum Cournot model with a general symmetric entanglement operator, exploring the effects of squeezing and phase parameters on game outcomes.

Findings

Entanglement degree's effect on payoffs is ambiguous.

Phase parameters significantly influence Nash equilibrium outcomes.

Maximum payoffs are limited when phase parameters are greater than zero.

Abstract

The properties of the Cournot model based on the most general entanglement operator containing quadratic expressions which is symmetric with respect to the exchange of players are considered. The degree of entanglement of games dependent on one and two squeezing parameters and their payoff values in Nash equilibrium are compared. The analysis showed that the relationship between the degree of entanglement of the initial state of the game and the payoff values in Nash equilibrium is ambiguous. The phase values included in the entanglement operator have a strong influence on the final outcome of the game. In a quantum duopoly based on the initial state of a game that depends on one squeezing parameter, the maximum possible payoff in Nash equilibrium cannot be reached when the value of the phase parameter is greater than zero, in contrast to a game that depends on two parameters.