Cooperative Advertising in a Dynamic Retail Market Duopoly

Abstract

Cooperative advertising is an important incentive offered by a manufacturer to influence retailers' promotional decisions. We analyze a retail market duopoly where one or both of competing retailers are supported by the manufacturer in their advertising costs. We model the problem as a Stackelberg differential game in which the manufacturer announces his shares of advertising costs of the two 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 the key drivers that determine the optimal subsidy rates and, in particular, obtain the conditions under which the manufacturer will support one or both of the retailers. We analyze the extent to which cooperative advertising coordinates the channel. Finally, we investigate the impact of an anti-discriminatory act which would restrict 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

JEL Classification: C61, C7, D43, M37