Network Formation in Competition Model

A competition model on a market is considered. Each player (firm) attracts customers only by price for a carriage service in a route network between any of its two nodes. It is proposed two types of players behavior: noncooperative and cooperative. In noncooperative scenario each player aims to maximize its profit in a route network, and as a solution concept Nash equilibrium is considered. In cooperative scenario it is supposed that two fixed players can cooperate only on a route which connects their hubs to maximize their total profit on the route, and on other routes their behavior as well as behavior of other players remains noncooperative. Here we refer to cooperative theory and choose a solution concept (core, the Shapley value). All considered scenarios are illustrated with a numerical example.