Title: A manufacturer-retailers dynamic cooperative advertising with retail competition

Authors: Peter E. Ezimadu; Chukwuma R. Nwozo

Addresses: Department of Mathematics and Computer Science, Delta State University, Abraka, Nigeria ' Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Abstract: This work deals with the cooperative advertising in a manufacturer retailers supply chain. It considers the manufacturer as the Stackelberg leader and the retailers as the followers playing a Nash game with each other. Using differential game theory it obtains a time consistent feedback Stackelberg equilibrium for the optimal advertising strategies and payoffs for a situation where retail advertising is subsidised and where it is not subsidised. The work shows that while the manufacturer's advertising effort reduces with subsidy, the retailers' advertising efforts and product awareness increase. These consequently lead to increase in all the players' payoffs. While a fair player would increase his advertising effort with increasing payoff, the others reduce their efforts. Further a retailer's advertising effort should be subsidised only if the rate of increase of the manufacturer's payoff through that retailer's margin to the manufacturer is twice greater than the rate of increase of that retailer's payoff.

Keywords: supply chain; Stackelberg differential game; Nash differential game; Sethi's sales-advertising model; Ericson's extension of Sethi model.

DOI: 10.1504/IJOR.2019.096943

International Journal of Operational Research, 2019 Vol.34 No.1, pp.104 - 143

Received: 28 Sep 2015
Accepted: 13 Mar 2016
Published online: 14 Dec 2018 *

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