Cooperative Advertising in a Dynamic Retail Market Oligopoly
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Cooperative Advertising in a Dynamic Retail Market Oligopoly Anshuman Chutani · Suresh P. Sethi
Published online: 25 August 2012 © Springer Science+Business Media, LLC 2012
Abstract Cooperative advertising is a key incentive offered by a manufacturer to influence retailers’ promotional decisions. We study cooperative advertising in a dynamic retail oligopoly where a manufacturer sells his product through N competing retailers. We model the problem as a Stackelberg differential game in which the manufacturer announces his shares of advertising costs of the N retailers or his subsidy rates, and the retailers in response play a Nash differential game in choosing their optimal advertising efforts over time. We obtain the feedback equilibrium solution consisting of the optimal advertising policies of the retailers and manufacturer’s subsidy rates. We identify key drivers that influence the optimal subsidy rates and, in particular, obtain the conditions under which the manufacturer will not support the retailers. For the special case of two retailers we obtain insights on some key supply chain issues. First, we analyze its impact on profits of channel members and the extent to which it can coordinate the channel. Second, we investigate the case of an antidiscrimination act which restricts the manufacturer to offer equal subsidy rates to the two retailers. Keywords Cooperative advertising · Nash differential game · Stackelberg differential game · Sales-advertising dynamics · Sethi model · Feedback Stackelberg equilibrium · Retail level competition · Channel coordination · Robinson–Patman act 1 Introduction Cooperative advertising is a common means by which a manufacturer incentivizes its retailers to advertise its product to increase its sales. In a typical arrangement, the manufacturer A. Chutani () School of Management, Binghamton University, State University of New York, P.O. Box 6000, Binghamton 13902, NY, USA e-mail: [email protected] S.P. Sethi School of Management, The University of Texas at Dallas, Mail Station SM30, 800 W. Campbell Rd., Richardson 75080-3021, TX, USA e-mail: [email protected]
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contributes a percentage of a retailer’s advertising expenditures to promote the product. We consider a marketing channel involving a manufacturer and N retailers. We model the problem of the channel as a Stackelberg differential game in which the manufacturer acts as the leader by announcing its subsidy rate, i.e. its share of retailer’s advertising cost to each of the N retailers who act as followers and play a Nash differential game to obtain their optimal advertising efforts in response to the support offered by the manufacturer. Cooperative advertising is a fast increasing activity in retailing amounting to billions of dollars a year. Nagler [21] found that the total expenditure on cooperative advertising in 2000 was estimated at $15 billion, compared with $900 million in 1970, and according to some recent estimates, it was higher that $25 billion in 2007. Cooperative adve
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