Modeling the Effect of Advertising and Subsidy Transfer in a Three-Level Channel Using Game Theory

Subject Areas : Game Theory

Peter Ezimadu ¹ , Joshua Apanapudor ² , Sophia Ezimadu ³

1 - Department of Mathematics, Delta State University, Abraka, Nigeria
2 - Department of Mathematics, Delta State University, Abraka, Nigeria
3 - Department of Mathematics, Delta State University, Abraka, Nigeria

Received: 2022-08-19 Accepted : 2023-01-10 Published : 2022-12-01

Keywords: Supply Chain, Stackelberg game, Cooperative advertising, differential game, subsidy rate,

Abstract :

Most cooperative advertising works assume that subsidy is usually given directly to the retailer. This work addresses a three-level supply chain setting where advertising subsidy is transferable from the manufacturer to the retailer through the distributor, together with a situation where both the retailer and the distributor directly engage in advertising. The parties in the channel are considered to play an infinite horizon Stackelberg differential game with the manufacturer as the leader, and the distributor and the retailer as the first and the last followers respectively. The work studies the effect of subsidy on the players’ profits in a four-channel setting where both the manufacturer and the distributor do not subsidise advertising; the manufacturer’s provided retail subsidy is not transferred to the retailer; the distributor provides retail subsidy without the manufacturer’s involvement; and the distributor transfers the manufacturer’s provided subsidy to the retailer. It determines the players’ optimal advertising efforts, subsidy policies, and profits for the four channel settings. It also obtains the players’ appropriate subsidy limits. The work shows that the channel profits are best with the distributor’s participation, followed by transfer of subsidy setting, and worst with non-provision of subsidy by both manufacturer and distributor.

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