| Advertising plays a key role in the everlasting struggle for market success between rival firms. For this reason, determining the optimal advertising strategy is a central issue for nowadays managers. This thesis studies horizontal advertising competition in duopolistic markets. The Lanchester model of combat, a well-studied advertising model, is used to describe the competitive shifts in market shares between rival firms. To derive the optimal advertising strategies, we use the techniques related to differential/difference games framework. This thesis is divided into two major parts where the issue of optimal advertising in competitive markets is addressed.; In the first part, we determine the feedback Stackelberg advertising strategies of the Lanchester model. To our knowledge, this the first time that the issue of hierarchical play in horizontal competition is investigated in an infinite time horizon. Thus, we assume that the industry is formed of two firms, one of them being designated as the leader and the other as the follower. The follower sets her advertising after the leader has announced and committed her own. The relevant solution concept is then the feedback Stackelberg equilibrium which has the desirable property of being sub-game perfect. However, the equilibrium cannot be characterized analytically and we have to device an algorithm to compute a numerical solution. As an illustration, we apply our algorithm to the data set related to the Cola war and we show that this solution concept has an empirical merit.; In the second part, we consider a simultaneous play game. Again, the market dynamic is described by the Lanchester model of combat. Assuming that the players account for current values of market share when taking their advertising decisions, we device a numerical algorithm to compute the Markov perfect equilibrium advertising strategies. The main contribution of this study is that our numerical computation does not require the restrictive assumption of zero discount rate. This assumption, commonly used by previous research, results in significant mathematical and conceptual difficulties. Our findings confirm that the use of this assumption is inadequate in an infinite horizon setting. We finally propose a generalization of the single-instrument algorithm to study the issue of multiple advertising decision. |
