The free-rider in the quantum Stackelberg duopoly game

This article studies the quantum Stackelberg duopoly game where the leader player moves as a free-rider. It is found in this scenario that the quantities and payoffs in equilibrium are not far from those achieved when the leader moves according to the backwards induction principle, converging to the Pareto optimal solution as the entanglement factor increases. •High entanglement drives the equilibrium to the Pareto efficient solution in the quantum Stackelberg duopoly (QSD) game when the leader player moves as a free-rider (FR-QSD).•low entanglement, the first-mover advantage may increase in the FR-QSD if the follower knows that the leader is a free-rider, but ignores his actual move.•Entanglement influences the equilibrium in the QSD when the leader moves according to the backwards induction principle resembles as in the defensive FR-QSD.