Posted price profit maximization for multicast by approximating fixed points

We describe an iterative fixed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, find an optimal posted price mechanism-i.e., 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 function. We can then apply the non-linear Jacobi and Gauss-Seidel methods of coordinate descent. We provide proof of convergence to the optimum prices for special cases of utility distributions and tree edge costs.