Suboptimal Solutions to Team Optimization Problems with Statistical Information Structure

Network team optimization problems with statistical information structure are investigated. A team of n Decision Makers (DMs), each having at disposal some information (obtained, e.g., by measurement devices or by exit polls) and various possibilities of decisions, coordinate their efforts to achieve a common goal, expressed via a team utility function. Decisions are generated by the DMs via strategies, on the basis of the available information y1, . . . , yn that each of them has and in the presence of uncertainties in the "state of the external world’ x (which the DMs do not control). Such uncertainties are modeled via a joint probability density p(x, y1, . . . , yn). For these problems, optimal solutions in closed form can be derived only in special cases, so a methodology of approximate solution is proposed. Suboptimal solutions are searched for, taking the form of linear combinations of elements from sets of basis functions, possibly with adjustable "inner’ parameters. Upper bounds on the accuracy of such suboptimal solutions are obtained. The estimates are expressed in dependence of the number of trigonometric and Gaussian basis functions. The trade-off between the level of decentralization and the smoothness assumptions on the utility function and the probability density, required to derive the upper bounds, is investigated. Numerical results are presented for an instance of the network team optimization problem under study, which models optimal production in a multidivisional firm