Nash Equilibria of Co-Operative Advertising Programs with Advertising Threshold Effects

As an important advertising phenomenon which has been proven by previous empirical marketing research, the advertising threshold effect implies that advertising has little effect on sales when advertising investment is beneath a certain level. In this paper, we focus on a cooperative advertising program, in which a manufacturer shares part of its retailer’s advertising cost, to illustrate the impact of the advertising threshold effect. Dividing the advertisement efforts into national and local advertising, we propose a new advertising response model which can describe the advertising threshold effect well. Based on the advertising response function, we derive the manufacturer’s and the retailer’s equilibrium advertising investments when they play a Nash game. From the analysis we find that there are four possible Nash equilibria when we take the advertising threshold effect into account. We derive the sufficient and necessary conditions under which each of the four possible equilibria is a Nash equilibrium, and explain these conditions with examples from practice. Another interesting result is that there are two different equilibria when certain conditions are satisfied.