Game-theoretical transportation model with limited traffic capacities

$n$-person transportation game over a network $G(?,R,T)$ is considered. The players are in the vertexes $M$ of the network $G$. The aim of each player is to put a predetermined flow capacity to fixed vertex with minimal cost. The set of Nash equilibria is constructed. It is shown that the minimum total cost is achieved in a situation of Nash equilibria. In the second part of the paper we consider a cooperative model in which the players can not share the capacities of the edges.