Modeling Dynamic Cooperative Advertising in a Decentralized Channel

Abstract

This work deals with cooperative advertising in a manufacturer-retailer supply channel using
differential game theory. By considering the manufacturer as the Stackelberg leader and the
retailer as the follower, it obtains the Stackelberg equilibrium showing the optimal strategies for
both players and their resulting payoffs for both the subsidized and unsubsidized retail
advertising. It shows that in a decentralized channel the provision of subsidy increases the
awareness share. This implies an increase in the sum of the channel payoff, but strongly suggests
that subsidy should only be provided if the rate at which the manufacturer’s payoff is increasing
is twice greater than the rate at which the retailer’s payoff is increasing. It shows that an increase
in a player’s margin leads to increase in his payoff, and further observes that while a fair player
would increase his advertising effort as his profit margin increases, the other player reduces his
margin, with the exception that when retail advertising is subsidised, the retailer tends to reduce
his advertising effort for smaller increases in manufacturer’s margin, but increases it as the
manufacturer’s margin gets larger.

Keywords: Cooperative Advertising, Supply Chain, Sethi Model, Differential Game.