Analysis of the dynamics of duopoly models under state feedback advertising policies with switching

Abstract

Investigates the effect of competitive advertising policies in a proposed class of duopoly dynamic models, inspired on the classical Vidale-Wolfe model. A basic assumption is that the firm with a lower market share than its target market share level switches on an extra control effort in its attempt to reach and surpass its competitor. Dynamical patterns of the proposed models, subject to competitive advertising policies which are based on the observed state variable, are investigated. An associated performance index is calculated. This index in conjunction with the qualitative analysis of the dynamics should guide the management decision on advertising spending.