Stochastic cooperative advertising in a manufacturer–retailer decentralized supply channel

Abstract

This work considers cooperative advertising in a manufacturer-retailer supply chain. While the manufacturer is the Stackelberg leader, the retailer is the follower. Using Sethi model it models the dynamic effect of the manufacturer and retailer's advertising efforts on sale. It uses optimal control technique and stochastic differential game theory to obtain the players' advertising strategies and the long-run value of the awareness share. Further, it models the relationship between the payoffs of both players and the awareness share. The work shows that with the provision of subsidy the retail advertising effort increases while the manufacturer's advertising effort reduces. It further shows that the total channel payoff is higher for subsidised retail advertising. However, the subsidy can only be possible if the rate of growth of the manufacturer's payoff is twice higher than that of the retailer.

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

“…Kermani et al (2012) applied game theory to study a supplier-selection considering price, quality and delivery performance. Ezimadu and Nwozo (2017) used game theory to consider a supply chain in which both the manufacturer and retailer are involved in national and local advertising, respectively. For a detailed look at the application of game theory in supply chain management, the reader can consider Kermani et al (2012) and Ezimadu and Nwozo (2017).…”

“…Dynamic models on cooperative advertising appear to be more realistic since they are based on the long-term relationship among a lot factors representing various individual interests of the players involved in the channel. These models employ differential game theory (Chintagunta and Jain 1992;Jørgensen et al 2003;Karray and Zaccour 2005;He et al 2011;Sethi 2012, 2014;Ezimadu and Nwozo 2017).…”

“…Such models include He et al (2009), Chutani andSethi (2012). Recently Ezimadu and Nwozo (2017) extended He et al (2009) to consider a situation where both the manufacturer and retailer are directly involved advertising while the manufacturer subsidises the retailer's local advertising expenditure.…”

Decentralized supply chain network design: monopoly, duopoly and oligopoly competitions under uncertainty

“…Also this is usually related to operational characteristics and leads to Nash game; most of the dynamic games in SC literature are unconstrained models that solved by differential systems (Xiao and Yang 2008;Zhang 2006;Dias 2010, 2013;Sinha and Sarmah 2010;Friesz et al 2011, Jain et al 2014Chen et al 2015;Nagurney et al 2015;Mousavi et al 2016;Santibanez-Gonzalez and Diabat 2016;Hjaila et al 2016a;Jahangoshai Rezaee et al 2017;Lipan et al 2017). (3) Competition with foresight: in this competition, the rivals show reactions to the entry of new comer in sequential manner and usually this is related to strategic characteristics; this competition leads to bilevel or multi-level models and stackelberg games (Drezner and Drezner 1998;Plastria and Vanhaverbeke 2008;Kucukaydın et al 2011, Zhang and Liu 2013Yue and You 2014;Zhu 2015;Drezner et al 2015;Taleizadeh and Charmchi 2015;Yang et al 2015, Esmaeilzadeh andTaleizadeh 2016;Hjaila et al 2016b;Aydin et al 2016;Ezimadu and Nwozo 2017;Genc andGiovanni 2017. Eiselt andLaporte 1997;Krass and Pesch 2012 have done a review of this kind of competition.…”

“…Ezimadu and Nwozo (2017) used Sethi model to models the dynamic effect of the manufacturer and retailer's advertising efforts on sale and by the help of control technique and stochastic differential game theory the players' advertising strategies and the long-run value of the awareness share are obtained. Esmaeilzadeh and Taleizadeh (2016) proposed the optimal pricing decisions for two complementary products in a two-echelon supply chain composed of one retailer and two manufacturers under two scenarios.…”