Cooperative advertising and pricing in a manufacturer-retailer supply chain with a general demand function; A game-theoretic approach

• Supply chain coordination via cooperative advertising and pricing is investigated.
• A relatively general demand function in a manufacturer-retailer channel is proposed.
• The cooperation game is strongly found to be infeasible.
• The manufacturer does not contribute in inefficient local advertising.
• Manufacturer’s margin is always lower than retailer’s in Stackelberg retailer game.

The manufacturer participating in a cooperative advertising scheme reimburses a percentage of local advertising expenditures to encourage the retailer into more promotional initiatives. The present study aims to investigate the supply chain coordination through cooperative advertising and pricing by proposing a relatively general consumer demand function. Based on the underlying balance of power among supply chain members, four possible game structures are discussed including the Nash, Stackelberg retailer, Stackelberg manufacturer and cooperation games. Moreover, numerical simulations are provided to exemplify implicit optimal solutions of the Stackelberg retailer-manufacturer games while they will also be used for comparison of the four games. The unprecedented results obtained from this study may be summarized as follows: (1) the cooperation game is strongly found to be infeasible depending on the certain channel’s parameters; (2) contrary to previous findings, the manufacturer’s margin is found to be always lower than the retailer’s in the Stackelberg retailer game; (3) in the Stackelberg manufacturer game, the manufacturer prefers to advertise nationally rather than to support local promotional activities when retailer advertising becomes inefficient; (4) we find that the manufacturer’s price is entirely stable compared to classical linear model and increases as effectiveness ratio of national to local advertising increases.