In search of a way to securely transfer information, the scientific world uses entanglement with several qubits. However, the experimental feasibility of implementing communication protocols remains unclear. In this work, we indicate a one-to-one correspondence between a quantum dialogue and the quantum Stackelberg duopoly game. If we consider a controller-dependent communication protocol to be a sequential quantum game, the two players, Alice and Bob, can be compared to two firms, $A$ and $B$. Moreover, the controller Charlie can be assumed to be the arbiter. First mover advantage is a significant feature of the Stackelberg duopoly game, which is explained and proved in the protocol. Further, we propose a controller-independent bidirectional quantum dialogue using four-qubit maximally entangled states. The efficiency of the protocol is determined to be 50$\%$.

为了寻找安全传输信息的方法，科学界使用多个量子位的纠缠。然而，实施通信协议的实验可行性仍不清楚。在这项工作中，我们指出了量子对话和量子斯塔克尔伯格双头垄断游戏之间的一一对应关系。如果我们将依赖于控制器的通信协议视为顺序量子游戏，那么两个玩家，Alice 和 Bob，可以与两个公司进行比较，$A$和$乙$。此外，控制者查理可以被假定为仲裁者。先发优势是Stackelberg双寡头博弈的一个显着特征，协议中对此进行了解释和证明。此外，我们提出了一种使用四量子位最大纠缠态的独立于控制器的双向量子对话。协议的效率确定为50$\%$。