A game theory–based model for dental centers in a competitive market of dental tourism under government intervention

The aim of this paper is to propose a mathematical model for two dental centers in a competitive market of dental tourism. Dental tourists are looking for cheaper treatment with proper quality, and dental centers are looking to maximize their profits by providing services to tourists. Government also monitors dental centers by setting tariffs (subsidies or taxes). This problem is modeled and solved in the form of Stackelberg (or Leader-Follower) game. The government as the leader determines the amount of tariffs and then the dental centers as the followers simultaneously determine the price and quality level of their services. To solve the game, first the equilibrium values related to the price and quality level of the services of the dental centers have been calculated by Nash equilibrium. Then, according to the equilibrium values obtained for dental centers, the optimal amount of tariffs are calculated. Finally, to clarify the proposed model a numerical example is provided and sensitivity analysis is performed on some parameters. In this paper, for the first time a mathematical model is developed for pricing and determining the quality of services in a competitive market of dental tourism. The obtained results indicate that increasing the amount of subsidy will lead to a decrease in the prices of service provided by the dental centers. Moreover, by increasing the amount of subsidies allocated to the dental centers, the government can expand the dental tourism industry.