Sorger game under uncertainty: Discrete case

Abstract

At the present time, the discrete-time models are not given enough attention. But these models are more realistic than the continuous models, because the allocation of funds is discrete. In the paper a new discrete model of optimal advertising is proposed. This model takes into account the uncertainties. These uncertainties are caused by acts of a set of the small companies. The companies’ problem is to maximize their market share taking into account the reaction of competitors. The problem is a discrete multistep optimal control problem. For this model the optimal control problem is solved explicitly. The Bellman method of dynamic programming is used to construct the guaranteed equilibrium.