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Chinese Physics Letters

Quantum Stackelberg Duopoly with Continuous Distributed Incomplete Information

Xia Wang, Chengzheng Hu

Published Dec 1, 2012• 14 citations
Publisher

Abstract

A general model of the quantum Stackelberg duopoly is constructed by introducing the "minimal" quantum structure into the Stackelberg duopoly with continuous distributed incomplete information, where both players only know the continuous distribution of the competitor's unit cost. In this model, the cases with complete information, discrete distributed incomplete information, and continuous distributed asymmetric information are all involved. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits some new interesting features, such as the total information uncertainty can counteract or improve the first-mover advantage according to the value of the quantum entanglement. What's more, this general model will be helpful for the government to reduce the abuses of oligopolistic competition and to improve the economic efficiency.

DOI
10.1088/0256-307x/29/12/120303

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A general model of the quantum Stackelberg duopoly is constructed by introducing the "minimal" quantum structure into the Stackelberg duopoly with continuous distributed incomplete information, where both players only know the continuous distribution of the competitor's unit cost. In this model, the cases with complete information, discrete distributed incomplete information, and continuous distributed asymmetric information are all involved. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits some new interesting features, such as the total information uncertainty can counteract or improve the first-mover advantage according to the value of the quantum entanglement. What's more, this general model will be helpful for the government to reduce the abuses of oligopolistic competition and to improve the economic efficiency.
The minimal quantization structure is employed to investigate the quantum version of the Stackelberg duopoly with continuous distributed asymmetric information, i.e. the first mover has incomplete information that obeys a continuous distribution while the second mover has complete information. It is found that the effects of the positive quantum entanglement on the outcomes exhibit many interesting features due to the information asymmetry. Moreover, although the first-mover advantage is counteracted by the information asymmetry, the positive quantum entanglement still enhances the first-mover advantage and improves the first-mover tolerance of the information asymmetry beyond the classical limit.
A more efficient model of the quantum Stackelberg duopoly is proposed by using the asymmetric quantization scheme of Qin et al. In this model, two entanglement factors α and γ are introduced, which greatly expands the functions of the previously reported symmetric one. By choosing proper values of α and γ, one can better manage the market, such as suppressing the first-mover advantage and enhancing the second-mover profit to avoid abuse of oligopolistic competition, and optimizing the total quantity of the products, so to overcome the deficiencies of "first mover always wins" and "positive quantum entanglement always reduces the total quantity" in the symmetric model. The proposed model here is believed to be a good tool for the government and the department to improve the economic efficiency and develop the market.
最小的量子化结构被采用与连续分布式的不对称的信息调查 Stackelberg 市场由两家卖主垄断的局面的量版本，即当第二 mover 有完全的信息时，第一 mover 有服从连续分布的不完全的信息。结果上的积极的量纠纷的效果由于信息不对称现象展出许多有趣的特征，这被发现。而且尽管第一行动的优点被信息不对称现象抵抗，积极的量纠纷仍然提高第一行动的优点并且在古典限制以外改进信息不对称现象的第一行动的忍耐。
We study Bertrand's duopoly of incomplete information. It is found that the effect of quantum entanglement on the outcome of the game is dramatically changed by the uncertainty of information. In contrast with the case of complete information where the outcome increases with entanglement, when information is incomplete the outcome is maximized at some finite entanglement. As a consequence, information and entanglement are both crucial factors that determine the properties of a quantum oligopoly.