Dynamics of Duopoly Models with Undecided Clients under Decentralized Affine Feedback Advertising Policies

Abstract

This paper extends the Deal-Vidal-Wolfe and Lanchester models of duopoly dynamics, which involve two populations, by explicitly introducing a third population of undecided users. An analysis of these extended models establishes conditions for the existence of equilibria, as well as their stability properties under different classes of advertising policies. This analysis also leads to the surprising result that the extended Vidale–Wolfe and Lanchester models, despite having different dynamics, under the general class of decentralized affine feedback advertising policies have equilibria in identical locations, with the same stability properties.