Optimal Advertisement Spending in a Duopoly with Incomplete Information

This article presents the relationship between a firm's advertisement spending and sales in a duopoly when information about the competitors' advertisement spending is unavailable. The competitive interaction between the firms has been modeled as imperfect information Cournot and Stackelberg games and the conditions for subgame perfect Bayesian Nash equilibrium are presented. The results suggest that when the firms are similar in size and advertisement effectiveness, both firms are better off sharing their advertising plans with each other. On the other hand, when one of the firms is a market leader, the follower may profit from the leader's advertisement spending and so is better off keeping the leader guessing. A practical approach to estimate the optimum advertisement budget based on the expected values of the competitors' historic advertising spending is presented as well.