Profit-maximizing multicast pricing by approximating fixed points.

We describe a xed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, compute prices to oer the users in order to maximize the expected pro t of the service provider. We show that any optimum pricing is a xed point of an eciently computable map. In the language of classical numerical analysis, we show that the non-linear Jacobi and Gauss-Seidel methods of coordinate descent are applicable to this problem. We provide proof of convergence to the optimum prices for special cases of utility distributions and tree edge costs.