Posted price profit maximization for multicast by approximating fixed points

Authors:
Aranyak Mehta;Scott Shenker;Vijay V. Vazirani
Affiliations:
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332-0280, USA;ICSI, 1947 Center Street, Suite 600, Berkeley, CA 94704-1198, USA;College of Computing, Georgia Institute of Technology, Atlanta, GA 30332-0280, USA
Venue:
Journal of Algorithms
Year:
2006

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Abstract

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.