profit-maximizing multicast pricing by approximating fixed points [extended abstract]
We describe a fixed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, compute prices to offer the users in order to maximize the expected profit of the service provider. We show that any optimum pricing is a fixed point of an efficiently 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.
multicasting fixed point profit maximization