Title: A mathematical model of cooperative advertising support to the followers in a manufacturer-distributor-retailer supply chain

Authors: Peter E. Ezimadu

Addresses: Department of Mathematics, Delta State University, Abraka, Nigeria

Abstract: This work considers cooperative advertising in a decentralised channel which involves a manufacturer, a distributor and a retailer. It uses Stackelberg differential game theory to model the direct involvement of both the distributor and the retailer in advertising, with the manufacturer supporting their advertising efforts through subsidy. The work uses Sethi's sales-advertising dynamics to model the market awareness share dynamics. It considers four channel structures and obtains the players' strategies and payoffs for all-four channel structures, and observes that the manufacturer should not totally subsidise any of the players' advertising effort. It further shows the manufacturer should not simultaneously support both players advertising efforts. However, if he must support both players, then a profit-sharing agreement on the channel payoffs must to be reached by the members of the supply chain to ensure that the manufacturer is not short-changed.

Keywords: cooperative advertising; decentralised channel; Stackelberg game; differential game; subsidy; Sethi's sales-advertising dynamics; advertising support; supply chain.

DOI: 10.1504/IJOR.2022.123450

International Journal of Operational Research, 2022 Vol.44 No.2, pp.141 - 170

Received: 27 Mar 2019
Accepted: 27 Jul 2019
Published online: 20 Jun 2022 *

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