Co‐op advertising in randomly fluctuating markets

Abstract

We consider a dynamic Stackelberg game between a manufacturer and a retailer facing a randomly changing market environment (boom–bust cycle) modeled as a Markov process over time. The manufacturer announces the national advertising effort and a cooperative (co‐op) advertising subsidy, and the retailer sets the local advertising effort. We derive the optimal feedback equilibrium advertising strategies and show that the channel members are forward‐looking in their advertising decisions. In the single‐crisis case, both the necessary and sufficient conditions for a positive subsidy reveal that the subsidy decision hinges on the relative profit margins before and after the crisis. Our comparative statics analysis indicates that the presence of national advertising enriches the members' advertising behaviors significantly. Furthermore, the pre‐crisis (post‐crisis) aggregate advertising contribution of the supply chain generally decreases (increases) in the damage rate and the crisis likelihood, as in the single‐firm case. But the individual advertising behaviors of the members may exhibit richer structures, depending on the comparative advantages of the members in each state. In addition, our numerical studies demonstrate that channel members can suffer sizable losses when they adopt myopic advertising strategies over their regime‐switching counterparts. Finally, we extend our analysis to incorporate retail and brand competition and show that the channel members' advertising behaviors are reasonably consistent with those without competition.