Co-op Advertising and Pricing in Randomly Fluctuating Markets

We consider a dynamic Stackelberg game between a manufacturer and a retailer facing a randomly changing market environment over time modeled as a Markov process. The manufacturer announces the wholesale price and a cooperative (co-op) advertising subsidy, and the retailer sets the retail price and advertising effort. The carry-over effect of advertising is modeled by a regime-switching extension of the Sethi model. We derive the optimal feedback equilibrium pricing and advertising strategies analytically and show that the players behave differently under four cases. The players are forward-looking in that they incorporate the expectation of potential switch of the market state into their strategies, which is in stark contrast to their behavior in a stable market. In addition, the switching likelihood and damage/recovery rate between the market states have a profound impact on the manufacturer’s advertising subsidy. The crossover interactions generally hold that advertising subsidy increases in the switching likelihood and damage level from good to bad market states, but it decreases with stronger intensities and recovery of the reverse transitions. In particular, our model indicates that when the damage level is sufficiently high, the manufacturer is vigilant about possible business failure and it may reduce advertising subsidy accordingly. Finally, the product-harm analysis can well fit into our framework as a special case