Bilateral "pricing" for consultation companies' competition considering customers' switching behavior

Customers are either eager or obliged to switch from a physical consultation firm to an online consultation platform. Considering customers' switching behavior and competition effect on bilateral users, the paper developed a three-echelon Stackelberg game framework where two consultation companies decide bilateral "pricing" (the service price and the wage), and the servicer decides service investment. In four scenarios combining two salary strategies (Employment or Sharing strategy) and two game sequences (firm as leader or follower), stakeholders' optimal decision-making and revenue were proved. We then theoretically analyzed the influence of some parameters on the equilibrium status and the gap between them and numerically simulated the joint effect of switching rate and parameters on the equilibrium revenue of stakeholders. It is deduced that in the consultation service market: (a) there is equilibrium status in all four scenarios when the switching rate, the servicer's sensitivity to current revenue, and the service cost coefficient on the firm satisfy certain conditions; (b) the servicer's potential market and the service investment cost coefficients negatively affect the optimal fixed wage set by the two companies and the servicer's revenue; (c) two consultation companies can achieve greater revenue when both adopt Sharing strategy; (d) servicer with higher perceived service cost are incented to devote more to servicing when both employ Employment strategy.