A mathematical model of the effect of subsidy transfer in cooperative advertising using differential game theory

Abstract

This work deals with subsidy transfer from a manufacturer to a retailer through the distributor in cooperative advertising. While the retailer engages in local advertising, the manufacturer indirectly participates in retail advertising using advertising subsidy which is given to the distributor, who in turn transfers it to the retailer. The manufacturer is the Stackelberg game leader; the distributor is the first follower, while the retailer is the last follower. The work employs differential game in modelling the effect of subsidy on the individual and channel payoffs; and models the awareness share dynamics using Sethi’s sales-advertising model. It obtains Stackelberg equilibriums characterising four-game scenario: no subsidy from neither the manufacturer nor the distributor; withholding of manufacturer’s subsidy by the distributor; provision of subsidy by the distributor in the absence of the manufacturer’s participation; and the participation of both the manufacturer and distributor in retail advertising. It shows that in the absence of subsidy from the manufacturer, the distributor should intervene by providing subsidy to the retailer. However, if this is impossible, he should avoid withholding the subsidy meant for retail advertising. The players’ payoffs as well as the channel payoff are worst with non-participation of both the manufacturer and the distributor, and best with transfer of subsidy.