Research on Government-Enterprise Regulation of Online Car-Hailing Based on Differential Game

Abstract

In the Internet era, with the widespread application of digital technology, the way people travel has changed. Compared with traditional taxis, more and more people prefer to choose online car-hailing. The rapid development of the online car-hailing industry has solved the problem of taxi-hailing to a certain extent, but it has also brought some new problems. To change the dilemma of the online car-hailing industry, it is necessary to strengthen the regulation of the online car-hailing industry. In this study, we consider the regulatory system composed of a local government and an enterprise and use the differential game to study the regulation of online car-hailing. In the Nash non-cooperative game, Stackelberg master–slave game, and cooperative game, we, respectively, investigate the indicators, such as the optimal regulatory effort of the government, the optimal regulatory effort of the enterprise, the optimal benefit function of the government, the optimal benefit function of the enterprise, the optimal benefit function of the system, the optimal trajectory of the service quality level for the enterprise, and the optimal trajectory of the goodwill for the enterprise. Moreover, we analyze the corresponding conclusions through examples. We obtained some important results. (i) In the Stackelberg master–slave game, the optimal ratio of the local government subsidy to the enterprise's regulatory cost is only related to the benefit distribution coefficient and has nothing to do with other factors. Moreover, when the benefit distribution coefficient is >1/3, the local government is willing to share the regulatory cost of the enterprise. Otherwise, the local government refuses to share the regulatory cost of the enterprise. (ii) Compared with the Nash non-cooperative game, the optimal regulatory effort of the local government remains unchanged in the Stackelberg master–slave game, but the optimal benefit of the local government increases. Moreover, when the benefit distribution coefficient is >1/3, both the optimal regulatory effort and the optimal benefit of the enterprise increase. (iii) Compared with the Stackelberg master–slave game, in the cooperative game, the optimal regulatory effort of both government and enterprise increases, and the system's optimal benefit also increases. (iv) From the Nash non-cooperative game to the Stackelberg master–slave game and then to the cooperative game when the benefit distribution coefficient is >1/3, the service quality level and goodwill of the enterprise all increase.

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“…With the goal of maximizing the Nash product P of the distribution proportion of each body, a revenue distribution model based on Nash negotiation is established, as shown in formula (17). where s * j and s ' j are the most ideal and the least ideal distribution proportion of the j-th body respectively, as shown in formula (18); wj is the distribution weight of the j-th body. The Lagrange multiplier method is introduced to solve formula (19).…”