Equilibrium in transportation game

A non-cooperative $m$-person transportation game which is related to the queueing system $M/M/m$ on graph is considered. There are $m$ services (transport companies) which serve the stream of customers with exponential distribution with parameters $\mu_i$ $i=1,2,\ldots,m$. The stream forms the Poisson process with matrix of intensities $\Lambda$. The solution of the problem of pricing and determining the optimal intensity for each firm in the competition is derived.