Network pricing using game theoretic approach

We model the interaction between the network and the network users as a noncooperative game and study the Nash equilibrium points (NEP) of the game. We show that there is a unique NEP of the game in our model with generalized power functions as the benefit function, and that the Nash mapping from the price vector space to the feasible system flow configuration space is both continuous and injective. We discuss how the network, an active player, can drive the users into an efficient state, by using a pricing mechanism. The convergence result for both synchronous and asynchronous schemes for a simple network is proved when users adopt a variation of the greedy algorithm. We also demonstrate that the results proved in this paper depend on the natural properties of the benefit functions, not on the particular form of the benefit functions used in the paper. The results proved can be applied to more general benefit functions.