Pricing and Transportation Costs in Queueing System

A non-cooperative four-person game which is related to the queueing system $ M/M/2 $ is considered. There are two competing stores and two competing transport companies which serve the stream of customers with exponential distribution with parameters $\mu_1$ and $\mu_2$ respectively. The stream forms the Poisson process with intensity $\lambda$. The problem of pricing and determining the optimal intensity for each player in the competition is solved.