Cooperation in transportation game

Anna V. Melnik

Contributions to game theory and management, Tome 8 (2015), pp. 223-230

Résumé

We consider a game-theoretic model of competition and cooperation of transport companies on a graph. First, a non-cooperative $n$-person game which is related to the queueing system $M/M/n$ is considered. There are $n$ competing transport companies which serve the stream of passengers with exponential distribution of time with parameters $\mu^{(i)}$, $i=1, 2,\dots,n$ respectively on the graph of routes. The stream of passengers from a stop $k$ to another stop $t$ forms the Poisson process with intensity $\lambda_{kt}$. The transport companies announce the prices for the service on each route and the passengers choose the service with minimal costs. The incoming stream $\lambda_{kt}$ is divided into $n$ Poisson flows with intensities $\lambda_{kt}^{(i)}$, $i=1, 2,\dots,n$. The problem of pricing for each player in the competition and cooperation is solved.

Détail

Keywords: Duopoly, equilibrium prices, queueing system.