Title: Optimal advertising model in a dynamic marketing with competing brands

Authors: Ming Yang Zhou; Jie Lin

Addresses: School of Economics and Management, Tongji University, Shanghai, 200092, China ' School of Economics and Management, Tongji University, Shanghai, 200092, China

Abstract: We consider a marketing channel consisting of one retailer and two independent and competing manufacturers. One distinctive feature of this paper is that each brand's goodwill evolves according to a modified Nerlove-Arrow dynamics, in such a way that the advertising effort of one brand hurts the competitor's goodwill stock. We obtain the feedback advertising equilibrium policies for the retailer and manufacturers in explicit form for a linear demand formulation and assess the impact of the margin profit and intensity of brand competition on these strategies in different settings. Then the results between the Stackelberg model and cooperative model are compared. Numerical examples show the paths for the evolution of the demand function and for the profits of channel members through the computation of the goodwill state variable trajectory and reveal that the brand competition coefficient has different effects on strategies.

Keywords: supply chain management; SCM; differential games; optimal advertising; brand competition; dynamic marketing; competing brands; modified Nerlove-Arrow dynamics; Stackelberg model; cooperative model; cooperation; goodwill.

DOI: 10.1504/IJMTM.2015.066779

International Journal of Manufacturing Technology and Management, 2015 Vol.29 No.1/2, pp.116 - 137

Received: 31 Oct 2013
Accepted: 21 Apr 2014
Published online: 05 Jan 2015 *

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